Donkey Kong Country Returns/Tropical Freeze
TimeSplitters/2/Future Perfect
Psychonauts
Super Mario Odyssey

I think Yooka Laylee was very similar to Banjo-Kazooie, the only real complaint I had in relation to it was that it focused on a few really big worlds instead of a larger amount of somewhat smaller worlds.

That said, I played it maybe 6 months after it was released, so from what I've heard it had gotten a lot of quality of life patching in that time.

I don't see that so much. When I think of a Rare shooter, I think of a mission-based, mostly-linear shooter with extensive local multiplayer options.

Rare's style was losing popularity since DK64. Even then, I still really enjoyed Starfox Adventures and Kameo.

As for what the OP is asking, I'd say:
-Max and the Curse of Brotherhood
-Super Lucky's Tale

...I can't think of any more!

timesplitters is an obvious choice, even longer missions with different difficulty was so typical rare and no other game did?

While the reviews to Yooka were average, I've been playing it the last few days and I really have to say if you want N64 platformer action from Rares glory days, it's exactly what you get, really nice characters, worlds and music... the only downside is they also seem to be absolutely bogged down with N64 camera type issues which I hadn't really been that nostalgic to want to experience again in 2018.

If you loved DK64 and Banjo Kaz though, I would give Yooka a look, and it's €/$10 off right now on the Switch.

A hat in time is an Indie, but it was highly praised when it came out, to the point that I've heard people say, 'why play Yooka-Laylee now, when we have an actual good collectathon platformer?'

It released very shortly before Mario Odyssey though and got lost in the excitement a little.