In WT-9881 a small change was made to set the flush time for tiered storage. Currently that change uses conn->ckpt_most_recent. Another suggestion was to use session->current_ckpt_sec.

What exactly are these two very similar values?
Are they always the same? If yes, can we remove the session one?
If no, what are the differences and when are they different?
Which is the right value to use for conn->flush_most_recent?

The session->current_ckpt_sec was added in WT-5927 (making checkpoint cursors work again).