Preface: The issue is no longer occurring. I have no idea what caused it, and I also have no idea how I fixed it, but I figured this might still be useful information regardless so I'll just explain exactly everything I did in detail. Also, I'm using Chrome and have a fair few extensions installed, but I tested it with all my extensions completely disabled and nothing changed so I doubt they affected it.
I haven't used this site before, so I first used manual input on the wish counter to plug in some numbers. I set the values for lifetime pulls, 5* and 4* pity for Character Event, Weapon Event, as well as Standard. I then signed into google drive, authorized everything, and put in all my characters in the Character tab. Then, I went back to the Wish Counter and hit the +10 button for Character Event, selected Nahida and hit Add, but nothing happened. I tried hitting Skip as well, but still nothing. I then noticed that, suddenly, the image for Nahida in the selection box had broken, replaced with the "image failed to load" icon. Now, for some reason, any time I went to either the Wish Counter or Home pages, the site completely broke. None of the buttons actually did anything and any data like "20.1K Nilou" or "19% from all 5*" never loaded, instead replaced with "...%" or just a loading symbol (shown in 1st attached image). Most notably though, if I tried to navigate to a different part of the site, it firstly wouldn't work, but curiously it would replace the URL in the URL bar with the one for the page I was trying to go to (i.e. on Home the url was "paimon.moe", but after clicking Settings the page didn't change at all, completely identical to if I hadn't clicked the button, but the URL in the bar was now "paimon.moe/settings").
The first thing I tried was clearing my cookies for the site, which worked, but the site would break in exactly the same way again once Google Drive synced my data. I didn't realize clearing cookies wouldn't log me out of google drive, but it doesn't do that I guess. Also, on the Wish Counter page, similarly to "20.1K Nilou" not loading correctly, even though it said "Data has been synced!" every wish counter was at 0 and the global rank stuff was also broken (image 2). I then tried messing around with the site after disabling google drive and clearing my cookies again and it worked perfectly fine, so I assumed the data in my drive was corrupted or something. Not being very familiar with google drive myself, I couldn't find where the site was storing the data to delete it, so I just stayed signed out and put in all my wish info manually again. I tested the wish counter again with another +10 and it worked, adding 10 to the totals when I hit skip (but the add button still doesnt seem to actually do anything I guess?). Crucially, I then went back to settings to log back into google drive to test the bug some more and discovered that I was already logged in, but it hadn't synced yet. I thought I had been signed out at that point but I could be wrong, but regardless this is the point where the bug magically fixed itself and now the site seems to be working perfectly.
Note: I didnt realize until after fully writing out this report, but the character screen may have been working correctly despite the wish and home screens being broken? I took the three attached screenshots in order while the bug was active, with the character screen being last (image 3), and yet it fully loaded my synced data despite this being after multiple different cookie wipes and google drive logouts/logins. This could've been when the bug was fixed, I have no clue.
I'd be happy to provide any further information if needed, and also I'm really sorry if this report isn't actually useful in any meaningful way and I just wasted your time with it.