I think that's very nice translation. The text isn't easy to translate, because some phrases aren't typital in Polish language - probably for better rythm and as a poetic devices. "zatańczymy się w sobie do lata" (literally "we will dance into ourselves until summer") is not grammatical form of this verb, but sounds like a "zakochamy się w sobie" (we will fall in love with each other) and for me this phrase means "zatracimy się w tańcu ze sobą aż do lata" (we will lose ourselves in the dance until summer). Pretty metaphor.
"And the glow... Has swelled with the need to break the silence" - it is too literall translate. First, basal meaning of word "nabrzmiały" is "swollen", but second mean is parallel "it is full of something" or "it is tense because of...". Better translation:
"And the glow that illuminates my hands as I write
Has full of the need to break the silence"
And off course, the glow is metaphor of poet's inspiration/afflation
"dziobi się w dziobów końcach a w ogonach ogoni" - in this context "dziobić" and "ogonić" are neologisms, verbs created on the basis words "beak" (of bird) and "tails". For me it is poetic image "my inspiration filled crows from beaks to tails".
LLM are getting better at translation and are beginning to understand certain types of neologisms and metaphors, and are also beginning to create their own to convey meaning, but they are still not perfect. Unfortunately, poetry in Polish is often very difficult to translate, especially the more formally classical kind. For this reason, it is difficult to popularize the poems of my favorite poet, Leśmian, (which are also often sung by bands similar to the one above)