Tested with just your two addons enabled.
BlizzardBags_ItemLevel
BlizzardBags_BoE

They both work fine with default bags, but combined bags are a no-go.

ItemLevel continues to show, but BoE disappears.

There are no errors given, just BoE text missing.

I've played around with it a little bit but I'm unable to reproduce the issue... Oddly, the BoA labels are missing for me in any form in the bags while BoE labels are there.

I've played around with it a little bit but I'm unable to reproduce the issue... Oddly, the BoA labels are missing for me in any form in the bags while BoE labels are there.

To expand further on the issue, if you first go from default bag UI into combined bag view the labels will show up, both ilvl and BoE, but if you set combined bag and then /reload - the BoE labels will cease to show.

So I've tried going from combined to separate and then from separate to combined with reloads of UI in between and cannot seem to make it not show consistently.

I did made it happen right after the loading, while everything is being indexed so if open the bags in the first few seconds after loading in... the labels are missing but as soon as I close the bag and open it again (or perhaps a few times of close/open), the BoE labels are back...

BoA labels still MIA completely. Correction: I've dug through the code... There's no BoA bind type which is what addon is looking at; referencing BoA in documentation is incorrect.