I think what you saw is normal. Beech often naturally hold onto their leaves all winter. Typically it’s the lower ones.
The tree's I had seen were holding all of their leaves. From top to bottom, young and old trees alike. I had read that some think lower leaves are held on the young trees to help protect new buds from deer. To be honest, I'm unfamiliar with beech trees, I don't have them in my area. I have read that they, along with some oak species, have marcescent traits.
The thing I noticed about oaks and beeches is there is a lot of variation within any given species about the timing of when they finally drop their leaves. There’s a pin oak 2 houses down from me that drops them around mid-February, but the pin oak I drive by downtown a mile away holds on to them until late April. Same thing with the beeches. There’s a lot of inconsistencies between individuals in different locations, and sometimes within the same stand. As far as I know nobody has figured out why this is the case. In general the beeches around here don’t seem to hold on to their leaves this late into the season though. Spring obviously comes a bit later in Maine than it does here in southern New England, so maybe that’s normal for them, I can’t really say.
The beech that I seen in the woods in Southeast Connecticut are all looking bad. Maybe 5% of the leaves I’ve come in the spring and all of those look bad.
I saw some Beech understory that appeared totally dead yesterday. Not a single leaf. As I recall I first noticed it there in the fall of 2021. It’s all looking bad but this was the first I’ve seen that was dead.