At this point I want to say thanks to everyone involved here! I'm absolutely blasted by how helping each one of you is! Never expected that I would receive so many helpful comments! Thank you very much.
The bad-gateway error is gone and I have no idea why, I basically killed the programs listening on port 80 and 443 because it started complaining about 443.
Now it complains that I'm not authorized. This should be an easy one, no? But. I didn't find anything in the caddy docs or in this community related to how to get there, would you have any ideas? I warns me that I didn't provide my email, but it looks optional and just providing that probably won't solve an authentication error anyways.
2021/08/06 05:06:33.512 INFO tls.issuance.acme.acme_client trying to solve challenge {"identifier": "ripped.link", "challenge_type": "http-01", "ca": "https://acme-v02.api.letsencrypt.org/directory"}
2021/08/06 05:06:34.960 ERROR tls.issuance.acme.acme_client challenge failed {"identifier": "ripped.link", "challenge_type": "http-01", "status_code": 403, "problem_type": "urn:ietf:params:acme:error:unauthorized", "error": "Invalid response from https://ripped.link/.well-known/acme-challenge/NL4Yw3d-6W09RJK0FZzbDlYyfhkGCRKCc2X45UUWkzE [80.89.217.226]: \"<html>\\n <head>\\n <title>Welcome to your SWAG instance</title>\\n <style>\\n body{\\n font-family: He\""}
2021/08/06 05:06:34.960 ERROR tls.issuance.acme.acme_client validating authorization {"identifier": "ripped.link", "error": "authorization failed: HTTP 403 urn:ietf:params:acme:error:unauthorized - Invalid response from https://ripped.link/.well-known/acme-challenge/NL4Yw3d-6W09RJK0FZzbDlYyfhkGCRKCc2X45UUWkzE [80.89.217.226]: \"<html>\\n <head>\\n <title>Welcome to your SWAG instance</title>\\n <style>\\n body{\\n font-family: He\"", "order": "https://acme-v02.api.letsencrypt.org/acme/order/130671497/14867960250", "attempt": 1, "max_attempts": 3}
2021/08/06 05:06:36.415 INFO tls.issuance.acme.acme_client trying to solve challenge {"identifier": "ripped.link", "challenge_type": "tls-alpn-01", "ca": "https://acme-v02.api.letsencrypt.org/directory"}
2021/08/06 05:06:37.460 ERROR tls.issuance.acme.acme_client challenge failed {"identifier": "ripped.link", "challenge_type": "tls-alpn-01", "status_code": 403, "problem_type": "urn:ietf:params:acme:error:unauthorized", "error": "Cannot negotiate ALPN protocol \"acme-tls/1\" for tls-alpn-01 challenge"}
2021/08/06 05:06:37.460 ERROR tls.issuance.acme.acme_client validating authorization {"identifier": "ripped.link", "error": "authorization failed: HTTP 403 urn:ietf:params:acme:error:unauthorized - Cannot negotiate ALPN protocol \"acme-tls/1\" for tls-alpn-01 challenge", "order": "https://acme-v02.api.letsencrypt.org/acme/order/130671497/14867967370", "attempt": 2, "max_attempts": 3}
2021/08/06 05:06:39.141 ERROR tls.obtain could not get certificate from issuer {"identifier": "ripped.link", "issuer": "acme-v02.api.letsencrypt.org-directory", "error": "[ripped.link] solving challenges: ripped.link: no solvers available for remaining challenges (configured=[tls-alpn-01 http-01] offered=[http-01 dns-01 tls-alpn-01] remaining=[dns-01]) (order=https://acme-v02.api.letsencrypt.org/acme/order/130671497/14867972870) (ca=https://acme-v02.api.letsencrypt.org/directory)"}
I don't know why it gets an "Invalid Response". I guess SWAG is coming from caddy itself. I will ask them how to fix that.
It works now. My initial problem was, that I wasn't verified with my data at AWS (weird, because I own other domains and those worked for the same computer).
The rest of the problem was my home computer being misconfigured (SWAG instance was some service that was started by something else, didn't had this problem on another machine). Thanks to everyone involved!