It may actually be slightly better. Itâ€™s a full wizard with bow proficiency with some nature spells ( I think they get light armor proficiency too). I think they also have some features of sharpshooter at higher level like ignoring some cover.
They donâ€™t get the ability to ignore cover, and level 5 isnâ€™t a straight upgrade for them like it is for other classes (they get doubled cantrip damage but are still encouraged to use the bow due to higher hit rate and better average damage, when everyone else gets double attack or actually do fully benefit from the cantrip upgrade). But they do get the Archery fighting style, which is what pushes them from a mere wizard with a bow into scary ass archer with even scarier full wizard spell progression. Borrowing a few Ranger spells like Goodberry (food is actually really important in Solasta) and Hunterâ€™s Mark is just the cherry on top.
Theyâ€™re a super fun utility caster otherwise, even if the other homebrew archetype Shock Arcanist is way stronger (I think they get the ability to automatically upcast cast certain spells by 1 spell level with no limit?). Greenmage is still far and above the most popular Solasta archetype purely for their sheer utility and the swapping between bow and spell playing style though. Itâ€™s a niche that doesnâ€™t exist anywhere in official 5E.