Does the parish priest have the authority to forbid communion in the mouth due to COVID pandemic? Does the parish priest have the authority to forbid communion in the mouth due to COVID pandemic, if he does not have explicit permission from his bishop? Note that I am not saying that the bishop would be against the decision of the parish priest, but just that he had not made any announcement (say for example that it is just probable that the bishop would agree with him).
Does the parish priest have the authority to forbid communion in the mouth due to COVID pandemic?
The short answer is no.
But there is a caveat to my response, which I am sure will not go down smooth with some of those who are very traditional.
A priest, of his own accord, can not refuse to give any faithful communion on the tongue and require that they receive Our Lord on the hand. Communion on the tongue is the norm within the Catholic Church and communion on the hand is permitted only by indult or special permission.

[92.] Although each of the faithful always has the right to receive Holy Communion on the tongue, at his choice, if any communicant should wish to receive the Sacrament in the hand, in areas where the Bishops’ Conference with the recognitio of the Apostolic See has given permission, the sacred host is to be administered to him or her. However, special care should be taken to ensure that the host is consumed by the communicant in the presence of the minister, so that no one goes away carrying the Eucharistic species in his hand. If there is a risk of profanation, then Holy Communion should not be given in the hand to the faithful. - Redemptionis Sacramentum

Thus it is obvious that communion on the tongue is our ecclesiastical right and no priest has the authority to change that fact on his own merits.
The faithful have the right to receive Communion in the hand or on the tongue. (See the article on Guidelines on Sacraments and Pastoral Care.)
Ultimately the pope could require communion on the hand due to a pandemic as a temporary measure to stop the spread of the coronavirus. It is highly doubtful that any pope would go that route.
Many dioceses have special protocols in place in regards to communion in regards to the present Covid-19.
Here are the new guidelines for the Archdiocese of Vancouver, where I live:

Reception of Holy Communion within Mass
In coming forward to receive Communion, physical distancing in single file must be maintained in the procession, though members of the same household need not do so.
As far as possible, all aisles should be only for one-way traffic.
It is recommended that the dialogue between the minister and the communicant take place with two metres separating them. The communicant bows to the minister, who says, “The Body of Christ,” to which the response “Amen” is given. The communicant then steps forward to receive Communion in the usual way.
The minister should take special care not to touch the faithful in any way (hand, tongue, etc.). If the minister senses that his fingers have touched the communicant or that the communicant’s hands have touched him, he should pause, place the ciborium on the corporal, purify his fingers in the ablution cup and then use hand sanitizer. The ablution cup should be cleansed after each Mass. The minister should repeat this process as often as he judges necessary during the distribution of Communion. It is not necessary, however, for the minister to use the ablution cup and hand sanitizer between each communicant, unless he makes actual physical contact.

I will admit that that there have been priests in our archdiocese who have refused the faithful communion on the tongue because of the virus. To this I have pointed out the new guidelines for the archdiocese and that he does not have the ecclesiastical authority to alter the norms that the archbishop has put forth.
This would be fine to leave the issue here and move on, but the whole story does not end here.
I am not going to get involved with the whole situation of the church-state, but a few lines need to be addressed here.
In some countries communion on the hand has been imposed by various governments due to concerns about the present pandemic, such as Germany. In this case the bishop might not explicitly tell the priest that state laws must be kept. Many are in favour of this, but not all.

In a letter to The Tablet this week the chairman of the Latin Mass Society, Joseph Shaw, observed that it was not permitted to distribute the host on the hand at the Extraordinary Form, and that in parishes where this was made mandatory, only the priest would consume. He also said that there was no objective medical foundation for suspending reception on the tongue.
Professor Jim McManus, Director of Public Health, who has advised the Bishops’ Conference on their response, told The Tablet: “The guidance is consistent with the fact that coronavirus is spread through saliva. That is backed up by studies which show that the virus has been consistently detected in the saliva of 91.7 per cent of patients.”
Mgr Basil Loftus, in another letter for The Tablet, said that it was urgent that the bishops forbid the giving of Communion on the tongue. - Coronavirus dispute over communion on the tongue

Matters of this nature are always reserve to the Holy See. Bishops must defer any questions to Rome on these matters. However, our present Holy Father seems to simply state indirectly that in countries which are ordered to give communion on the hand by government health rules pertaining to the present health situation are to obey those same governmental requirements.

Pope Francis waded into the church-state debate about virus-imposed lockdowns of religious services, calling Tuesday for “prudence and obedience” to government protocols to prevent infections from surging again.
Francis’ appeal came just two days after Italian bishops bitterly complained that the Italian government offered no provisions for Masses to resume in its plan to reopen Italian business, social and sporting life starting May 4.
While it wasn’t clear if Francis intended to send a different message than the bishops, his appeal for obedience and prudence was in line with his previous calls to protect the most vulnerable, and for economic interests to take a back seat to shows of solidarity.
At the same time, Francis has certainly chafed at the lockdown, saying early on that he felt like he was in a “cage” and lamenting more recently that the church isn’t really “Church” without a community of faithful present and the administration of sacraments.
“As we are beginning to have protocols to get out of quarantine, let us pray that the Lord gives his people, all of us, the grace of prudence and obedience to the protocols so that the pandemic doesn’t return,” Francis said Tuesday.
Francis' weekly Sunday blessings from his window overlooking an empty St. Peter’s Square, not to mention his solo Holy Week and Easter services, have served as a stark visual reminder of how the pandemic has radically altered the practice of communal religious observance around the world.
Some Catholic conservatives and traditionalists have bristled at the closures and framed them as a violation of their right to religious liberty. Some evangelical pastors in the U.S., Brazil and elsewhere have resisted lockdowns and held services, and big religious observances in South Korea, France and Iran have been been blamed for helping to spread the infection early on. - Pope urges virus lockdown obedience amid church-state debate

The pope in simpling asking the faithful to obey. He has not stated that they must obey quarantine requirements. But logic dictates that that the majority of the faithful will heed the words of Pope Francis.
To obey the government rules of lockdown, does not mean that we can not challenge these same rules through dialogue with various levels of government. Legal steps within the courts have already been done by some Catholic Bishops already in various countries.
The following articles may be of interest:

Can We Be Required to Receive Holy Communion in the Hand, Because of the Virus?
US Bishops Approve Communion on the Tongue