The speaker begins with something reassuring: her partner knows about her depression and anxiety, and he tells her she's all he worries about. That should be comforting. But the poem quickly turns on the word "But," and a quieter fear comes through. She wonders whether her illness might eventually push him away.
Notice how she tries to talk herself out of it. "I don't think that will happen" sounds calm, almost like a reminder she is repeating to herself. Then the final line, "But that's what anxiety does to a person...." undercuts that calm. The trailing dots make it feel unfinished, as if the worry doesn't really end, it just fades out for a moment.
The mood is tender but uneasy. There's real love in the poem, yet also doubt that even kind words can fully quiet. The speaker seems to recognize her fear as part of her anxiety, and still can't switch it off.