I think membership in the Federation are worlds, not species. The 150 number from Star Trek: First Contact is in response to a question from Lily about how many planets are in the Federation. Take that and Picard's response for what you will, of course.
The only other evidence I can think of with regards to species vs. worlds/polities is in the 32nd century on Discovery, there are obvious human citizens of the Federation, but Earth itself is not a member.
Except for the premise that First Contact movie established the idea that UFP is spread over 8000 Ly's.
There cannot possibly only be 150 planets in the whole Federation because that's just NONSENSE.
There are 971 stars within 50 Lightyears. The space within 1000 Lightyears is 8000 bigger than that... so you could expect between 7 to 8 MILLION Stars in just 1000 Ly's radius.
Given the UFP is spread over 8000 Ly's, we're looking at least at 56 MILLION stars. So, in that amount of space (8000 Ly's), there are over 150 warp capable species (and some pre-industrial ones) that comprise the Federation in the 24th century.
151 warp capable species represent 0.00027% in that amount of space (not counting pre-warp ones).
Even TNG established there are MANY uninhabited M-class planets within Federation space.
Worlds in this case (that comprise the UFP) refer largely to alien SPECIES original evolutionary planets - colonies not included ... I'd say that mass migrations between member planets hadn't happened until the later half of the 23rd century.
Separate individuals can be Federation citizens whether or not their member planets are part of UFP.
Earth not being part of UFP in the 32nd century has little merit here because it was a founding member and humans spread to the stars just before that (with most Humans living largely on Earth, in the solar system, others going on freighters, Starfleet etc.).
So while Earth as a planet is not part of UFP in the 32nd century (and therefore individuals who live on Earth aren't Federation citizens), in the grand scheme of things, there are humans outside of Earth who ARE Federation citizens... so provisions would be left for individuals of species planets who left the UFP so that those individuals would retain their Federation citizenship if they wanted to remain in the Federation.
But if you meant it in a different way... before the UFP was founded (and some time after that), most species just occupied their native planets and colonies (very little or no inter-species mixing or species living on each other origin planets and colonies).
Since UFP, various migrations would occur and 4 different species would intermix with each other and become citizens of Earth, Andor, Vulcan, Tellar, etc. (aka, Burnham was a citizen of Vulcan/Ni'Var) and so forth... but she was part of SF/UFP as well.
So, in this context, sure, worlds is wouldn't necessarily represent exact number of species , but you still have about over 150 different alien species living on each member planet (depending on the atmosphere) and inter-mixing, living and working together by the 24th century... by the 31st (prior to the Burn), you'd be looking at a pool of 350 species.
Planets by the 32nd century would have plethora of different species on a single member planet sure... but I largely count in the 24th century 'worlds' as individual species by their name ... more or less... but even in this century, each member planet would have any variety of other alien species working and living there and being citizens of Earth, Andor, Tellar and Vulcan for example and on a larger scale, citizens of UFP... but you're still probably looking at a pool of 150 different Warp capable species across those member planets.
Some individuals from outside UFP could have requested asylum and become Federation citizens, so the number of species could actually be GREATER than 150 in the 24th or greater than 350 in the 31st century... but again, when looking in the context of inter-species mixing... most species before joining the UFP and maybe sometime initially after joining would have stuck to their own (with some smaller migrations initially and later on moving onto more migrations).
But heck, even representatives of that planet in the 32nd century with the Butterfly people ended up being of the same species (not mixture of other species - which is what you'd expect by the 32nd century - a mixture of species on each previous member planet - and even planets who were never members of UFP to begin with).
Even Trill seemed to have only been populated by Trill only. Earth on the other hand had a more diverse amount of aliens living there.