He feels like Spike is stealing his whole identity
I think that's right but I'm not sure to what extent Angel has his own identity. Identity is to a large extent external...it's given - which is why identity can be stolen (and why it's funny when you're represented by a "lobster"). My passport identifies who I am: my height, my nationality; my age. I offer it as proof of who I am. However, I can feel "taller"; I can act "my age" - or not; I can feel "younger". I can feel as much European as British. The latter is self - "me" not I. That said, there's an overlap.
When Buffy says "he's not my boyfriend but he's in my heart" Angel should be worried.
Throughout, people constantly identify (or misidentify) Spike as Buffy's boyfriend. They impose an identity on him (and by association her) from the outside. For Buffy to internalise him, to take him to heart is a much more intimate relationship than boyfriend because it cuts out a third party. To a large extent, it's the message of Touched, which is kinda groundbreaking. As a sense, touch is immediate: the moment you touch someone, they touch you back. It does away with subject/object. She's embodied him; he's part of her self - not part of her identity (which was a major problem in S6). He doesn't stand in for her, he doesn't "represent" her as a passport does. He's inside her. In fact, we've come full circle from S6. "I know you felt it ... when I was inside you..." but we're on a different level. Spike saw red; Angel's seeing green. Kinda clever when you think about it.
In contrast to this closeness, Buffy "basks" in Angel...you bask in the sun and the sun's a bloody long way away...as are the baked cookies. Still love...but of a different type.
How else could Angel have responded? What's the opposite of jealousy? Indifference (wasn't going to happen) generosity (of spirit)? Could he have been happy for her? It's a running joke that Angel isn't generous and is morose...and I think running jokes in BtVS run deep. Jokes are "the royal road to the unconscious". The dictionary says "admiration...pride". It might be a negative emotion but I'm not sure how you can be jealous of someone without admiring what they have (or what they are). If I'm jealous of some one's dress, shoes, life-style, talent it's because I want it...perhaps want to be them.
Despite what people (and the bible say), I don't think jealousy or envy are "natural" or entirely negative emotions. They're cultural and I presume, for that reason, it's possible to have a social formation where they don't exist (and I suspect that state comes very close to primitive communism...or being dead). In fact, I don't see how consumer capitalism works without jealousy or envy in some form or other. For some schools of thought, "jealousy" and "possession" are an intrinsic part of love.
In Real Me, Buffy is envious of Dawn's relationship with Joyce (for very similar "internal/external; self/identity reasons). Riley tries to reason her out of it. Buffy replies.
BUFFY: Thank you, logic boy. Did I mention this is a rant? Sense really has no place in it.