Due to the Slice of Life preference, that's makes things incredibly tricky if you just want to stick with PS3. There's a lot of really great VNs on the PS3 like Steins;Gate and CLANNAD (including Toyoma After It's a Wonderful Life).
OH! SoniComi on PS3 may actually be a great one for you! It's pretty chill, is more than just a VN, and I never found the speech to be too fast, either. A great game overall, imho.
If you have capabilities to play on PC, this
really opens up options that I think are vital for learning Japanese through VNs. NEKOPARA volume 2 actually has the ability to display
both English and Japanese as the Language and Sub Language display (I
think vol 1 also had this feature retroactively implemented, but I cannot confirm atm). I think many DenpaSoft games also have this feature, too (and if you're worried about h-content, the non-h versions are on Steam, or your flavor of the seven seas yarharhar~). Image below is an example of what I'm referring to. (If you're not familiar with NekoPara, it really is basically a big ol' fluffy Slice of Life comedy that's not only
actually funny for SoL, but also really good SoL that I can approve of as someone who really dislikes SoL, in general.)
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Tokyo School Life is another really great example of this that's both on PC and the Switch that also allows for dual language display as shown above (iirc).
Though, IMHO,
Go! Go! Nippon! ~My First Trip to Japan~ should be a MUST PLAY for dual language display, and also because it's just an awesome VN, in general. It was also one of the first VNs I ever saw that did this and was ahead of the curve by nearly 10 years for dual language display.
I do hope this helps ya in the right direction in some way! Good luck on your endeavors! o7