We recently followed an almost identical upgrade path (however at the time PG16 wasn't yet supported by Timescale, so stopped at PG15 + TS 2.12).
We did look into using logical replication to reduce the downtime of the upgrade, but because database schema and DDL commands aren't replicated, it seems that it isn't recommended with Timescale in the loop.. (I suppose the underlying schema changes that Timescale needs to make under the hood are mostly a function of your hypertable chunk sizing and what your incoming writes look like, so this could be planned around / timed well, but we felt it added too much potential complexity & risk compared to simply opting for a small maintenance window while pg_upgrade completed).
We did look into using logical replication to reduce the downtime of the upgrade, but because database schema and DDL commands aren't replicated, it seems that it isn't recommended with Timescale in the loop.. (I suppose the underlying schema changes that Timescale needs to make under the hood are mostly a function of your hypertable chunk sizing and what your incoming writes look like, so this could be planned around / timed well, but we felt it added too much potential complexity & risk compared to simply opting for a small maintenance window while pg_upgrade completed).