Section 31 and Starfleet can't Time Travel.
What they can do is hunt down time travelers/Observers and take their gear, or conscript these future people into the current day war, or argue for a temporary truce because of aligned objectives.
They have a psych profile and biological profile on Daniels from Enterprise. It shouldn't be hard to find more "people" like Captain Daniels hiding in Starfleet's ranks.
I'd also look inside computer networks for back doors, retro viruses, weird coding language, and spotting the use of passwords in places the owners of those passwords would never use those passwords, that the future is using to control or monitor the past.
Here's the problem.
Current day Section 31 does no trust even future Section 31 or past Section 31 to use time travel responsibly, because altering time is destroying time (sometimes). You could dissolve for a paradox at any moment because you from 10 days ago is irresponsibly fiddling with time technology. If you can't trust yourself from 10 days ago not to burn the galaxy down, how can you trust some other asshole you never met upholding the cut throat policies of section 31, 4 centuries from now, to safe guard the web of time, and your present day Federation's place in it?
The Department of Temporal investigations finds offensive time tech and puts it in a vault. Section 31 should be treated like an alcoholic in a brewery by even and especially itself. Zero tolerance.