How did I overperform in this rapid tournament? My bullet rating is currently 1400 and it's pretty much the only time format I play as it is quick. I figured that I wanted to think my moves more thoroughly so I played some rapid games in a Lichess tournament. My rapid rating was around 1100, still having the "?,"  so you can imagine I wasn't playing much rapid.

I was amazed that I was able to beat 1800 players if I did not rush the moves. I even berzerked and won having 5 minutes to think. As black, usual features of the games were play on the kingside, opposite side castling, me having a bishop queen battery aiming at h3, and a rook on g8. Usually there is a white knight on f3 and a pawn on h3 and I gain initiative by playing g4 to force him to take with the pawn. They usually never make space to run with the king. Here is an example game.

Additionally, here is a different type of game in which my opponent blundered. Another game is also interesting even though my opponent’s rating wasn't high. I would definitely like you to take a look at it.

Was this just luck or I would be able to climb up someowhere around 1600-1700 if I played longed time formats?
There is a game theory of why 1st round NFL drafts don't perform as well as expected.  The reasoning is that the player had an above average couple of games and returned to his average performance.  By the same logic, there are later round drafts who have stellar careers.

I'm not going to make a judgement based on three games, or even your archive on lichess.org, as this would be as effective as making a prediction based upon your avatar.  I would say that guess that this tournament was lucky for you (assuming that your not a teenager who just improved naturally), but that, just by experience alone, you could achieve an 1800 rating on lichess.org at any time control.

EDIT:
Stacia Pugh (https://www.youtube.com/channel/UCn2k14U03rNRHApDIloxOkA) is a chess example.  She started off well and achieved a peak rating of 1791.  This can be considered a fluke as she quickly dropped to her floor rating.  She's still a good player and is trying to improve.