I'm not sure if you read his recent comment (from March) where he explains the reason for blocking the PR.

The reason so far is that there is no consensus on whether highway=busway should replace the additional tags one can add to indicate that a highway street is limited for buses only.

  > However, so far we are pretty far away from highway=busway replacing highway=\* + access=no + bus=yes as the consensus tagging for any and all bus only roads world wide. Hence my suggestion in #4226 (comment) still applies - solving #214, and in context of that think about rendering highway=busway in a way that reflects a distinct meaning (which would likely be in analogy to highway=pedestrian). A possible design approach to this is shown in https://imagico.de/blog/en/rethinking-road-access-restrictions-rendering/

So, no, it's not stagnated because the author wants it. A previous commit from one of the maintainers (jeisenbe) said the issue was closed because no consensus was obtained from the tag proposal, dated 2020:

  > I’m closing this for now because there is still no established way to tag these features. Once either service=busway or highway=busway (or some other tag) becomes established as the clear consensus of most mappers, we can reopen this issue.

https://github.com/gravitystorm/openstreetmap-carto/issues/4...

Ask anyone from the community and this is quite a good reason to block the addition of new features to the map style, especially if they aren't widely used and not standard.