How do an ability-setting item and a +1 feat interact?

Question

I'm playing a Half-Elf Lore Bard at level 5, with CON score of 14 after racial bonus.

Yesterday evening, a great oracle gave my character an Amulet of Health, which does the following:

Your Constitution score is 19 while you wear this amulet. It has no effect on you if your Constitution is already 19 or higher without it.

I'm quite happy as my character gain more HP, and my concentration checks will be improved.

In my initial plan, I wanted to take a feat at level 8: resilient (CON) which gives my character +1 CON. I still do, to at least gain the proficiency in Constitution.

If I take that feat, what will be my character's Constitution score? 19 or 20? Basically, how do a set ability score and a modifier interact?

When planning on D&D Beyond, it says my CON is 19, but is it correct? Why? Which rules are involved here?

Answer 1

It is 19

The amulet says:

Your Constitution score is 19 while you wear this amulet

So, your constitution score is 19.

It also says:

It has no effect on you if your Constitution is already 19 or higher without it.

But this is not relevant, because your Con without it is 15.

There are no other rules involved. The amulet is very clear on the point that the score is always 19 except if it was higher without considering the amulet.

So: you calculate your score without amulet (15). You put the amulet on, it becomes 19 because it was lower than that.

If you already had a score of 20, the second part would take effect, making the amulet not change anything.

Notice that the order in which the feat and the amulet are gained do not influence the calculation.

Answer 2

Your constitution is 19 when you have the amulet, 15 otherwise.

Your feat gives you +1 CON, which sets your CON score at 15. Specific beats general, so when you attune to the amulet, your CON is 19, no other modifiers apply.

Your Constitution score is 19 while you wear this amulet.

The order in which you attune or take a feat is not relevant. The feat gives you a permanent modifier to your base score. The item sets your current CON score, overriding the base value.