@DjinnFor Overall I'd say yes, it becomes less of an issue! It's been a little while since I actually read the books, but I'll try to give my honest thoughts from what I recall + some skimming.
that each book covered two ministories and neither had enough time to develop much depth for any of the characters involved
V3 is basically where the "real" plot begins - as in, a major thread starts there and continues to be woven for multiple volumes. Though there are indeed important pieces from V2 included moving forward as well, but just looking for a certain relevant keyword, its first appearance is in V3.
There's definitely a sizeable handful of names tossed around in V1, but I think the major cast's character count is acceptably stable after that, so you get more used to them as time goes on. They don't necessarily all get the same levels of depth given, but where in V1 you might be like "Show you the difference between Alan and Glen? ... They're the same picture," they'll be more distinguishable as individuals later.
To some extent, the "ministory" feeling won't leave entirely, because the author likes to put a side story at the end of each volume. And I won't deny sometimes I wish there was more of the main story instead of a side story. But there is indeed a main storyline that I've found considerably more gripping the deeper into it we go!
that the main princess character had little to no agency, and what little agency she had seemed artificially manufactured and totally unbelievable.
This is exactly the reason that V1 is my least favorite. For the most part she sits around while the plot happens around her, which isn't the best of reads. Looking back on the volume from the perspective of knowing Chris and Eli will be happy and lovey-dovey together, it's a fun lighthearted read, but I think the content was possibly more suited to having been an end-of-volume side story than the central focus.
Anyways, it's not like Eli's confidence issues poof away in a plume of smoke suddenly, but she does get chances to speak her mind - to discuss, disagree, and then decide for herself what she thinks she should do. She grows (both in terms of her as a person and her believability as a character!), and it's nice to see.
Skimming back over the volumes, I think if I were to say "read to here before you make a decision to continue," it would be to get through V3's main segment. If you read all the way through that and think "Eh, the story isn't for me," I wouldn't recommend continuing - but if you get there and say "Oh?? It's getting good??" then you should continue. Of course, three whole volumes can be a bit of a hurdle depending on the person, but alas, that's just how it is.
I admit, I stalled out on Bibliophile Princess during vol. 3
If you ever find the desire to check out the series again, I'd recommend trying to get through that volume's main segment in full and seeing how you feel ^^