A trustee-to-trustee transfer of an HSA where the funds are never paid to you is not reportable. However, if you instead receive a distribution from the original HSA and indirectly deposit it into the new HSA, this would be a distribution and rollover that would be reportable on your 2024 tax return but would be nontaxable. Such a distribution and rollover is permitted only if you have not done another distribution and rollover of an HSA within the one year period ending on the date of the withdrawal from the HSA. Age and Medicare coverage have no bearing on the permissibility of a distribution and rollover of an HSA.
