I wish there was a game that started as a point and click adventure. Expressing the main character as a normal person, who's struggling from depression. But after a certain point in the game, It switches to First Person. You play as the main character travelling in their own thoughts to the source of the problem. Someone who left them.
More of a remake or similar game to a game I've recently played called: You Left Me.
Depends on what constitutes a genre.
The "genre" list on itch reads
Action, Adventure, Card Game, Educational, Fighting, Interactive Fiction, Platformer, Puzzle, Racing, Rhythm, Role Playing, Shooter, Simulation, Sports, Strategy, Survival, Visual Novel
And if we want to have a switch in genres, or a mix up or containing several of those.
Most games that feature minigames might qualify.
I believe many have one genre on top of another. Like a shooter engine featuring puzzles. Prime example is Portal. That one even "changes" genres, depending on if you jump into the fire or not after the puzzles.
I am missing management and sandbox in that list. Sport games often have a manager aspect. You might play the sport events, but also have the management of your team. But I do not think this counts as changing genres, as it is meant to have both aspects simultanous.
If we wanna count them, many clicker/idle games somewhat change. They have a start phase that might count as action and then become something akin to optimisation strategy with so little action that you can literally idle or even offline play them.
Well there are old games I recall which has multiple genres in it. The best example I could give is Battletoads. I haven't played arcade version nor the newest one but the Genesis and SNES have different genre in each stage.
There's also Actraiser, which is primarily hack n slash platformer but it has management or strategy genre/mode in it.
The "problem" with your example is engines. You usually could implement any point and click story in a first person engine (and that one might even be capable of 3rd and 2nd person). And of course, many a first person engine game tries to have platformer elements to the dismay of some players that can't jump accurate in those.
What I would call a change is switching between turn-based and real-time. Those Pathfinder games can do that, but the switch is player chosen. Same as you can chose to play Skyrim in Ego perspective or zoom away to 3rd person.
