It doesn't say it counts as armor or natural armor or anything, so it doesn't. It's just 1 AC on top of everything else, to emphasize the sturdiness of Warforged. It should stack with everything and prohibit nothing.

To support this, note that the Warforged trait provides a bonus to AC, rather than setting it to a number, as armor is wont to do. The Tortle, another race with an armor-related ability, sets its armor class to 17 like armor usually does, and correspondingly disallows further benefits from wearing armor, further illustrating that abilities that provide bonuses to the class of worn armor (like the Warforged trait) are not armor and are intended to modify armor, while abilities that provide a different default armor class probably count as armor and definitely don't modify the effective class of worn armor.

These are approximately equivalent.

2 Skill proficiencies are more useful than a language overall (both in my experience and according to the rulebook in so far as you can train languages, but not skills, with the Downtime rules in the Player's Handbook), so you have to be careful, but losing your choice of a cantrip for one of the least useful ones (in my experience) should account for this discrepancy.

This can also be seen by comparing the Half-Elf and High Elf racial traits side by side (as these official races are roughly balanced with each other).

">" is slightly better than; ">>" is noticeably better than; ">>>" is much better than

\begin{array}{rcl} \bf\text{High Elf} & & \bf\text{Half-Elf} \\ \hline \text{+2/+1 ASI} & \text{<<} & \text{+2/+1/+1 ASI}\\ \hline \text{Fey Ancestry} & \text{=} & \text{Fey Ancestry} \\ \hline \text{Darkvision} & \text{=} & \text{Darkvision}\\ \hline \text{Extra Language} & \text{=} & \text{Included}\\ \hline \text{Keen Senses} & \text{≈} & \text{1/2 Skill Versatility}\\ \hline \text{Cantrip} & \text{>} & \text{1/2 Skill Versatility}\\ \hline \text{Trance} & \text{>} & \text{none}\\ \hline \text{Elf Weapon Training} & \text{≈} & \text{none}\\ \hline \end{array}

I consider Keen Senses and "skill of your choice" to be roughly equivalent since Perception is one of the more useful skills available from experience and WoTC Adventure Module analysis. Elf Weapon Training is a very minuscule benefit.

Now let's take your Sun Elf Homebrew and compare it in the same manner.

\begin{array}{rcl} \bf\text{Sun Elf} & & \bf\text{Half-Elf} \\ \hline \text{+2/+1 ASI} & \text{<<} & \text{+2/+1/+1 ASI}\\ \hline \text{Fey Ancestry} & \text{=} & \text{Fey Ancestry} \\ \hline \text{none} & \text{<} & \text{Darkvision}\\ \hline \text{none} & \text{≈} & \text{+1 Language}\\ \hline \text{Noble Heritage} & \text{<} & \text{Skill Versatility}\\ \hline \text{knows } light & \text{>} & \text{none}\\ \hline \text{Trance} & \text{>} & \text{none}\\ \hline \text{Elf Weapon Training} & \text{≈} & \text{none}\\ \hline \text{Celestial Resistance} & \text{>>} & \text{none}\\ \hline \end{array}

This hinges on the fact that Necrotic and Radiant are rarer damage types in your setting and that History and Persuasion are not used more often in your campaign. In a setting with heavy intrigue and/or many creatures that deal Necrotic or Radiant damage, this race may be unbalanced as Celestial Resistance is pushed to much better than status and/or Noble Heritage is roughly equivalent to Skill Versatility (I've not done any analysis on the proportion of campaign-styles where this is relevant like the WoTC balance team likely did, so I can't say for sure if this is balanced overall, but it seems to be).