To barkskin in 5e its supposed to working with dexterity bonus and shield as welll.
This is incorrect, sorry. In 5e, Barkskin is a buff which ensures that your AC cannot be lower than 16 - that is, it gives you an AC calculation method that is "AC = 16". It is a calculation method - you can only use one calculation method at a time, and they don't add or compile with one another.
What this means is that if you have 8 dex and no armour and a shield, and you cast barkskin on yourself, your AC becomes 16, if you use Barkskin's AC calculation method. If you don't, your other Ac calculation method is the standard method, which is 10 +dex mod +possible shield, and would, in this case, be 11. 16 is higher than 11, so it makes sense to use Barkskin and have your Ac be 16.
If, on the other hand, you have 20 Dex, leather armour and a shield, you have the standard AC calculation method with leather armour, which would give you an AC of (AC = 11 + Dex (5) + Shield (2) = 18), OR you can use Barkskin, which gives you the calculation method (AC = 16 = 16).
You cannot say "I have Barkskin, and leather armour, and 20 dex, and a shield, so isn't that '16 (bark) + 1 (leather) + 5 (dex) + 2 (shield)'?" because that would be mixing different Ac calculation methods together, which you cannot do.
Edit: in case I've misunderstood, you are correct that Barkskin should *Not* force your AC to be 16, and thus lower it, if your existing AC would be higher - it should not make the second example character's AC BE 16 - that character's AC should remain 18, and Barkskin would have functionally no effect unless their AC would otherwise drop below 16 (such as if they took off their armour and shield). If the game is currently *reducing* your already-higher AC
to 16, that is indeed a bug and should be reported.
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For the rest though, yes, lots of things aren't working as they should revolving around druids and wildshape - basically, Larian's code says "You become bear now! You are Bear!!" and forgets literally everything else.