I understand that an extra Feat is a big deal, but it seems to me that given the attributes changes put everything in line with V. Humans now, that feat isn't a big deal any more since most of the new races have things that are at least that good, but also tend to get another benefit or two as well. Am I missing something?
The power balance of Variant Human will always depend on the choice of feat.
Variant Human cannot be said to be strong or weak until you’ve made a choice of feat. It is usually referred to as a particularly powerful race because people generally assume one of the good feats will be selected, such as Sharpshooter, Sentinel, Crossbow Expert, Great Weapon Master, or Mobile, to name a few that are typically regarded as very good feats. If you choose an underwhelming feat when you pick Variant Human, then naturally, your racial choice will feel underwhelming. Be honest, have you ever considered selecting Weapon Master as your Variant Human feat?
Monsters of the Multiverse hasn’t changed this. None of the newly revised races are so good that they make Crossbow Expert feel underwhelming in comparison. The good feats are still good, the underwhelming feats are still underwhelming. The diversity of choices provided by Variant Human giving access to a feat means it will always be a relevant option - from the powerful combat options to the interesting thematic choices. It provides access to themes and mechanics no other race can. So it will always be relevant.
Solid, thoughtful answers above. I have a different take on it though, less to do with MoM changes. MoM made some other races more balanced and less likely to be banned (Yaun-ti for example). The variant human gets +1 to two different attributes of their choice, plus a feat. Presumably this is designed to make human a compelling racial option while thematically keeping with the idea that humans are very adaptable.
In my opinion, the more challenging question is did Tasha’s actually weaken or negate variant human. Tasha’s Cauldron of Everything introduced Custom Lineages. Basically, a new non-racial option. With custom lineage, players can play any humanoid character (flavored to be like any other racial species), and get +2 to a single attribute, dark vision or a skill, and a feat. The downside to this, is if you take a custom lineage and flavor it as an elf hybrid, you get NONE of the elf special abilities or traits. This is a major downside. However, humans don’t really have any special abilities. So a custom lineage human, technically isn’t a human, but who cares. Your not giving up much mechanically. So it then becomes, is +2 to a single attribute, plus dark vision, a better version of human variant. I would say yes for some single Attribute builds like a rogue, but variant human still has some use for multiple attribute builds like a paladin. Just my thoughts.