This mod already does give garrison units to any landmark that can recruit units, as well as many other thematic landmarks.

1) I specially checked T-5 Unique buildings Lotern and Gaean Valley - there is nothing there.
1.1) In the palace of the Phoenix King, neither Phoenixes nor Phoenix Guardians can be recruited.
1.2) In the gardens of the Eternal Queen, neither Sister Avelon, nor Servant, nor Forest Dragons can be hired.
1.3) In T-3, the unique port of Lothern, only Marine Guards without shields can be recruited.
2) I propose adding the ability for the High Elves to hire two different types of naval guards at T-3 normal ports.
3) I propose to add to the Dark Elves the ability to hire two different types of corsairs in T-3 normal ports.

I think there may be a language miscommunication here. This mod doesn't change what units can be recruited. This mod is about garrisons, not military recruitment. Almost all of those buildings will contribute units to the garrison because of this mod.

per your examples...
Lothern Port: Lothern Sea Guard
Court of Phoenix King: Phoenix Guard
Everqueen Court: Handmaiden

Is it possible to have garrison troops - in addition to characters - also gain veterancy?

Yes, it is. If I were to do that, that would likely be incorporated into Better Sieges rather than Reporting For Duty.
I've thought about it for some time. Better Sieges already gives the garrison troops a buff of +100% ammunition, 20% missile ward, 10% magic ward, and +15 Leadership. So I feel the need is largely met at this time.
In the future I'm likely to revisit the idea and alter the buff and incorporate increasing veterancy with the level of the settlement or another condition. But I have other things (including updates to this mod!) that I will do before.

Hello, I would like to ask if you would be so kind as to make a submod "Reporting for Duty" for this mod? - https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=2619991775
Detachments suitable for adding this faction to garrisons: Harpies, Dark Riders, Black Ark Corsairs. I would be extremely grateful for that:)

Possibly after I finish submods for OvN and The Amber Kingdom.

Is your mod compatible with CTT, or would it need a submod ?

https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=1214959308

Your question is answered in the mod description.

Sorry