A migratory lifestyle is associated with shorter telomeres in a songbird

Telomere dynamics are sufficiently different between mice and humans to be cautious about extracting meaning from mouse studies.

Birds have very much more different telomere dynamics.

So aside from that, average telomere length is typically measured in immune cells from a blood sample. Telomere length shortens with each cell division, and stem cells delivery new cells with long telomeres. So in immune cells you are going to get a fuzzy metric that depends on everything known to influence immune function filtered through a combination of immune cell replication and replacement rates. So stress, injury, exertion, diet, infection, age, etc, etc.

What you end up with is a statistical measure that can support any number of theories, being fairly distant from underlying processes, and influenced by many processes. There's a lot of variation in the literature, and many contradictory datasets and interpretations.

That again is entirely distinct from the evolutionary background that leads to a species having telomeres that start at a given length, and there are wide variations in that metric across species - just look at mice and humans.