Almost there.
I was struggling with Otacilia Severa coins, the reverse is matching (ΔΗΜΑΡΧ ΕΞΟΥϹΙΑϹ) but the lettering on the obverse not.
Then I changed my search filters on RPC to look for Antioch coins with the same reverse on other rulers and just got Herennia Etruscilla.
Whoever made the previous ID was on the right track but missed by a little.
Got the ID:
Herennia Etruscilla
249-251 AD
Tetradrachm
Antioch, Syria
Obv: ΕΡΕΝΝΙΑ ΕΤΡΟΥϹΚΙΛΛΑ ϹΕΒ; diademed and draped bust of Etruscilla, right, on crescent
(officina mark is a number of dots below the bust, yours I see two but there could be more)
Rev: ΔΗΜΑΡΧ ΕΞΟΥϹΙΑϹ, S C; eagle standing on palm, right, spreading wings, holding wreath in beak
There are various RPC IX entries for this type, both for eagle to left and right. Got 22 of them on the search results:
https://rpc.ashmus.ox.ac.uk/search/browse?volume_id=&number=&city_id=25®ion_id=&province_id=&subprovince_id=&reign_id=&person_id%5B%5D=50&obverse_inscription_simplified=&reverse_inscription_simplified=%CE%94%CE%97%CE%9C%CE%91%CE%A1%CE%A7+%CE%95%CE%9E%CE%9F%CE%A5%CF%B9%CE%99%CE%91%CF%B9&obverse_design=&reverse_design=&metal_id=&weight_min=&weight_max=&diameter_min=&diameter_max=&format=
Anyway, it is not on our catalog.
And I think we must create two pages, one for eagle to left on reverse and another for eagle to right.
On the Antioch catalog there are two Trajan Decius tetradrachms with these eagles (one for each orientation), we could use them as basis.