I

In this sentence "comme" is an adverb and it means "for". In French a synonym would be "en tant que".

• Halton’s Espace Francophone has for mission …

You can formulate that differently in English as

• "The mission of the Espace francophone of Halton is to …" or

• "Halton’s Espace Francophone’s mission is to …".

It happens that removing "comme" yields another syntax that amounts sematically to the same thing, so DeepL is right.

II

It is not easy to determine this from the sources such as the dictionaries. You have to match the pattern to what you find in the dictionaries (a comme mission de favoriser le … → Verb + comme + Substantif + Prop. infinitive), but that is easier said than done.