I know this is probably a bit niche but wondering what some of your favourite video games that has wet character models.

Personal favourite of mine is Tomb Raider

Leisure Suit Larry: Magna Cum Laude's had wet t-shirt levels with clothes going translucent

Hard to say as most wetlook is rather basic and doesn't really work that well with games that realistically. It'd be cool to see improvements made as it's one of the few examples I can think of when it comes to untapped potential for graphics in games since they've done just about everything else

I am still waiting for them to make a live action movie version of the 2000 video game "American McGee's Alice" a horror version of Alice in Wonderland. That game had wetlook swimming scenes. Sadly, 26 years later the movie version is still in limbo and not yet made. In 2001 Nightmare on Elm Street creator and director Wes Craven acquired the rights and Milla Jovovich and Christina Ricci were also rumored to star in the film version. By 2005 Craven eventually contracted Sarah Michelle Gellar to star in the film, but then everyhing fell apart and Craven dropped out and Sarah Michelle Gellar dropped out, and over the last 20 years the film has been stuck in limbo. Craven had since died and SMG is now way too old for the part. She did not have a good track record starring in live action versions of animated series anyway cos she failed to repeat any of the wetlook scenes that Daphne did in the original cartoon Scooby Doo series.

Maybe in the next few years someone will finally make that live action version of American McGee's Alice cos the swimming scenes in the computer game version are interesting.

When it comes to wetlook in games you do need to suspend your disbelief to varying degrees. Games usually reach a compromise on wetlook effects due to technical limitations or due to not being a very important aspect of the visuals unfortunately. Different games will highlight some properties of wetness over others and are not necessarily aiming for realism but instead delivering the impression that something is wet. Here are some games that incorporate wetness:

Tomb Raider
As you already mentioned. Anniversary and Legend do wet clothing quite well in that they're not shiny and instead highlight how dark clothing becomes when wet. The procedural drying from top to bottom is also the best that I've seen in any game because it even goes out of its way to dry stretched parts of the fabric sooner than creased points. Rise looks nice and has shine which highlights the microsurface of fabric but it dries very quickly which isn't completely unrealistic but limits the time you can see the effect out of the water. It also suppresses the shine while underwater.

Black Desert Online
The effect is pretty shiny on most clothes but the effect is also inconsistent across clothing items. Some clothes get extreme shine while on others it's barely visible. A nice bonus is some clothes go translucent when wet but only the ones that are flagged as "fanservice" which is unfortunate because a regular set of armour which is made of a material that should be translucent when wet is not. The drying effect works from top to bottom but is not as detailed as Tomb Raider Anniversary or Legend's crevice-based drying. Otherwise it does have nice swimming animations and lots of bodies of water which are readily accessible and a vast ocean with underwater places to explore.

SCUM
As a survival game that aims to be hyper-realistic, wetness and wet clothes have many gameplay implications in addition to visual effects. Every item has a wetness attribute and affects items differently. Non-waterproof clothing becomes extremely heavy making your movements slower and decreases accuracy, dries slowly and thick clothing like sweaters and jackets take even longer to dry. Wearing wet clothes decreases your body temperature relative to the ambient temperature and weather conditions increasing the chance of getting hypothermia. Wearing wet socks or shoes will increase your chance of becoming infected if worn too long over time requiring antibiotics to cure. The visual wet effect is subtle but effective and clothing takes a realistic time to dry relative to the weather conditions and if you're wearing it, how many layers, if it's hot, dry, by the fire, exposed to rain, humidity, etc. Sweat also causes clothing to increase in wetness slightly and layering wet clothes will cause the water to spread out between the layers over time. This also includes putting wet clothes in a backpack. If you're wearing a lot of clothes and jump in the water, you also just sink or swim slowly relative to your total weight.

Blue Guardian: Margaret
This is an H-Game from Japan where you navigate a flooded dungeon and fight enemies, many of which are tentacle-based (because of course they are). Despite the pixel art style, it incorporates wetness by making clothing translucent and taking damage also causes the clothing to rip. The gameplay incorporates long underwater puzzles where breath control and underwater combat is an important gameplay mechanic.

The Parasites
Another explicit survival game which is closer in graphics to SCUM but explicit like Blue Guardian: Margaret.

Honourable mentions:
Champions Online: Brief shine and drops applied when you leave the water for a few seconds.
Palworld: Just looks like you were dipped in plastic but matches the art style.
Atelier Ryza 2 and 3: Only reacts when you go underwater or in rain but the effect is nice.
Genshin Impact: Only has dripping effect when you leave the water but has gameplay implications.