Bonuses in general stack in 5e
Unlike in Pathfinder or 3e, there is no rule in 5e that bonuses of the same type do not stack. By default bonuses always stack, as long as they are caused by features that have different names.
This exception to stacking is on p. 252 DMG, Combining Game Effects:
Different game features can affect a target at the same
time. But when two or more game features have the
same name, only the effects of one of them - the most
potent one - apply while the durations of the effects
overlap. (...) Game features include spells, class features,
feats, racial traits, monster abilities, and magic items.
See the related rule in the "Combining Magical Effects"
section of chapter 10 in the Player's Handbook.
And, mirroring that on p. 205, PHB, under Combining Magical Effects, for spells in particular:
The effects of different spells add together while
the durations of those spells overlap. The effects of
the same spell cast multiple times don't combine,
however. Instead, the most potent effect — such as the
highest bonus — from those castings applies while their
Because in your case all the features have different names (Integrated Protection, Defense, Blessing of the Forge, Soul of the Forge), they all stack. Together with the 18 base AC for full plate and +2 from Shield they will get the character to 24 AC.