FUN token doesn't really react to that
The token price will react as BTC is the denominator which means when BTC is stronger especially sharply up on a particular day that should put pressure on that price. Same as prices are certain to rise when a currency value falls. So thats a definite relationship but I agree if people are positive on BTC it probably does help the FUN token price longer term. If we compare the recent low for FUN price in dollars and cents to the price today, its risen by 44% which is no small amount. To then want a Satoshi quoted price rising on top of that value gain would be exceptional, longer term I would estimate Bitcoin performing well raises the interest and requirement for 'safe harbor' of long term sites like this. Whatever the narrative I do think its a fairly good guess this site does well alongside bitcoin usage and market generally. However the price wont move immediately in parallel to BTC.
If an increase occurs in the BTC price, of course the pair on the FUN and BTC exchange market will decrease except for fiat currency it will increase, that's why never buy FUN using your BTC, if you hold BTC you should keep it well in your wallet, don't use it to buy tokens FUN, because if the price of BTC strengthens, of course the exchange on FUN tokens will decrease.
I think for beginners who don't understand calculations, never buy FUN as a long term investment using BTC, I mean if they have BTC, just hold on to it, but if they have fiat currency, they should buy FUN with fiat currency, because of course, if the price of BTC increases, the price will increase. FUN will also increase sharply on fiat currency.