Currently, there's only one submitted run on the Web version ("1 run" 6th place). The reason for this is clear - the mobile app is just a better game, with nicer looking visuals, more mechanics, and more maps.
I haven't played the mobile version much, but the speedrun times suggest some key mechanics must be different. I think a perfect time on Web is going to always be slower than, or very hard to equal, a good time on mobile. For example I think that a perfect "1 run" run on the Web version is probably around 15-17 seconds.
The reason I think this is the "Searching for players" waiting screen after you click Play, which spawns in a seemingly random number of bots at the same time as you and spawns in the rest while showing a loading wheel graphic. This can take up to 10-15 seconds, but if you get good RNG it can take less (look at the current Web run, that was really lucky as far as I can tell). You can be sitting on this false loading screen for the same amount of time it takes a good player on mobile to finish a level.
Also, gameplay mechanics like player speed and gravity may be different. I don't know.
Because of the lack of content on the Web version, the only current category that really applies is "1 run". However, you can beat 10 beach-style tracks (which are randomly selected) to complete the first level. After that there is no further progression. Beating these 10 levels takes about 5 minutes with a bit of practice and good RNG (track selection wise AND loading screen wise). Also, once you've played some, you have to clear the save data to go back to the start, which is annoying to do manually each time.
Here's my suggestion: Create a separate version category for Web. Have two run categories to start with, 1 run and Beach%.
I did say that clearing the save data is annoying. You have to open developer tools, access the Local Storage (which is in different tabs in different browsers), and reset current_level and win_level_cnt in the object AVK_AQUA_IO_DATA. However, I coded a simple browser extension (for Chrome and all Chromium-based browsers) that clears the save data for you.
It can also show you an approximate live timer and can read the save data to act as an autosplitter - meaning that at the end of the run it stops the timer and shows you your final approximate time. This triggers when the player's character hits the surface of the pool while swimming up, so a little bit before they can click the continue button. This can be used as an in-game time and the official time can be retimed using BetterSpeedrunTimer anyway. Or, that functionality can be disabled and leave the extension to just clear the save data. It also has random name setting that doesn't allow the player to change their name mid run - slightly overkill but makes it harder for splicers (but seriously, who's gonna splice in this game lol).
That's just my two cents on the matter. I'm interested to see what the (albeit small) community and moderator think!