Is there a military building in Apollonia?

Yes. And I cry recruit exactly the same troops in it.
30 turns later, the problem is still unsolved and I can't even replenish from Sparta itself. But I can merge my troops and recruit another one.
I tried another campaign with the Arverni : resplenishment is totally fine.

Have you been able to solve this problem? because i have it too, my armies with rome only replenish inside the city, not in the surrounding region

Yes !

After 60 turns, 3 armies, the same issue : no resplenishment.
Then, my faction leader dies.

The next turn, all my armies have full resplenishment. Not only the little "+", but the double "++" (to be clear with an example : +31 men per turn for a given unit group)

If I reload my save before my leader die and wait a few random turns for his death, suddenly, all the resplenishments work.

It seems that the leader had a faction-wide hidden stat and I can't find it in all his stats and modifiers.

Oh thats pretty ♥♥♥♥♥♥, because i am only a turn 20, my faction leader is not gonna die for some time, but thanks for the info

But the strange thing is, i was watching this youtuber lionheart. He started a DEI campaign a few weeks ago, and he doesnt have this issue. His armys replenish outside the citys too. And i have exactly the same submod with DEI as him

The correct experimental way should be to start a new campaign and see if the problem remains. Because each new campaign randomly generates some parameters such as characters attributes.

Your image lacks the supply info for the army but I can see its not due to lack of population in that region. DEI has lots of UI mouse over info

So if its not supply its one or more negative modifiers to replenishment.

Suggestion:
Swap out the general with the calm trait leading that army , calm gives -8% replenishment rate modifier at stage1. It will get less as general ages. These traits have 3 stages. stage 2 (aged ) its -6%, stage 3 (mature) its -4%

When garrisoned troops get a +8% replenishment bonus, which is why they do not replenish outside a settlement at present with that general. Alternative get more positive modifiers on that army. the yellow skill tree has some , as do some agents and stances and ancillaries.
The UI may not show replenishment until the following turn after u fix that.

Also other factors like seasonal effects, supply , buildings , enemy agents etc can also impact it.

The management (red) technology stages also provide faction wide replenishment bonus for each full stage (1,2,3) you complete.

Bottom line, if an army is not replenishing its due to either negative modifiers or lack of supply or population

If u can't work it out based on what I said I suggest you ask on their discord where u can post screenshots. Its much easier to troubleshoot there than here.

I have the same issue, though it seems random.

First, I started a campaign with Sparta and had no problem with it (units replenishing fine with starting faction leader).

Then, I decided to restart the campaign (new campaign, still with Sparta) and none of my units could replenish.
I'm not really gonna wait out for my faction leader to die so I guess I'll just wait for the fix.

Character attributes I suspect.
Most folks gloss over the political/character development side of Rome 2 + DEI.

It goes hard, deep and one can create a War Beast General, Population Boosting Loving General or a complete Ruthless bastid with negative traits that impact things like Pop Growth and Army Reps.

Another tip is Diplomats, hire them and check the stats, I aim for +Pop Growth with +Pop Order. Deploy them - every little helps!