Yes it makes so much sense they do not have a similar feel at all.
It gathered the reputation due to having the Richard cameo (though of course LA has heaps of contemporary Nintendo cameos) and being Japan only allowed the rumour to spread. I mean I imported a copy like ~20 years ago because I am a huge fan of LA and wanted to play the ‘related game’. I’ve still not played it through though, even with the translation.
Mario Kart 64 seems to be widely cited as the first game to include a distinctly named mirror mode that mirrors the game visuals, as evidenced by Google AI summaries parroting it:
Yep, and 2D racers definitely had mirror modes as well.
Perhaps an argument could be made that Mario Kart 64 was the first time a formal mirror mode became actual content that sat alongside the main game, but I wouldn’t be surprised if that was also done before as well.