I jumped ship to a tech lead job. Now I do what I always wanted which is to direct a team (dotted line) by scaffolding out the project using diagrams and shallow coding. Very few soul sucking status meetings. .Dream job and a nice 25% salary boost.
At a lot of companies the description you gave for "senior developer" would be described as a tech lead. In many other companies neither example you gave would line up to their terminology. And every possibility in between.
There's not much uniformity in titles and descriptions of roles.
A lot of companies mistake tech lead for "senior dev" or "dev manager" or some chimera of both.
Really sounds like that last job was just garbage and you moved on to someplace better. Had nothing to do with the position other than it wasn't the lead position you wanted.
And what you’ve said is 100% true.
In fact I'd encourage to do the opposite, describe the job activities and then map them to whatever mental model you have about dev career ladder.
If I decide to slow things down as I get older I may go back to just straight coding. I love it.
An organization that has a team lead constantly in meetings is horribly mismanaged; and is looking for a talking head to boost someones' ego.