I'm a native Swede but not exactly a grammar wizard.
"kommit" is past participle for the verb komma:
- "komma" = to arrive
- "kom" = arrived
- "har kommit" = have arrived
In order to say "I have arrived" in modern Swedish you'd say "jag har kommit". Or more commonly "jag har kommit fram" = "I have arrived (to my intended destination)".
"är kommen" might be passive voice in grammar terms(?), but in everyday use it will sound like an old-fashioned form of "har kommit". "kommen" would be similar to "cometh" in English. So saying "jag är kommen" would sound like "I hast cometh" or similar archaic form. So you wouldn't normally use that form or you'll sound theatrical and very formal.
Versions of "kommen" is mostly used as an adjective, something that has arrived. For example you have "ankommen" (verb and adjective both) which also means "have arrived" but is specifically used when arriving to a travelling destination. Or "hemkommen" meaning arrived home etc.
A phrase "sommaren är kommen" can still be used in modern Swedish when specifically referring to the seasons, though it will sound a bit formal. I'm guessing it's an old saying that has remained. You'll find it in a lot of traditional songs/psalms about spring or summer.
Informally, you'd rather just say "sommaren är här" = summer is here.