Have you looked into the mail log to see what is actually happening to single mails that stay in the queue?
Hello again, here is an excerpt from the mail log:
Sep 28 11:58:33 host postfix/smtpd[52308]: warning: dict_nis_init: NIS domain name not set - NIS lookups disabled
Sep 28 11:58:33 host postfix/smtpd[52308]: connect from 213162073012.public.t-mobile.at[213.162.73.12]
Sep 28 11:58:33 host postfix/smtpd[52308]: TLS SNI mail.example.at from 213162073012.public.t-mobile.at[213.162.73.12] not matched, using default chain
Sep 28 11:58:33 host postfix/smtpd[52308]: DC99415145D: client=213162073012.public.t-mobile.at[213.162.73.12], sasl_method=CRAM-MD5, sasl_username=
exampl@example.at
Sep 28 11:58:34 host postfix/cleanup[52314]: DC99415145D: message-id=<
df241097-d511-91c6-aa71-94d7a1df613e@example.at>
Sep 28 11:58:34 host check-quota[52317]: Starting the check-quota filter...
Sep 28 11:58:34 host psa-pc-remote[23246]: SKIP during call 'check-quota' handler
Sep 28 11:58:34 host spf[52319]: Starting the spf filter...
Sep 28 11:58:34 host spf[52319]: SPF status: PASS
Sep 28 11:58:34 host psa-pc-remote[23246]: PASS during call 'spf' handler
Sep 28 11:58:34 host dk_sign[52320]: Starting the dk_sign filter...
Sep 28 11:58:34 host psa-pc-remote[23246]: PASS during call 'dd51-domainkeys' handler
Sep 28 11:58:34 host postfix/qmgr[23294]: DC99415145D: from=<
example@example.at>, size=635, nrcpt=1 (queue active)
Sep 28 11:58:34 host postfix/smtpd[52308]: disconnect from 213162073012.public.t-mobile.at[213.162.73.12] ehlo=1 auth=1 mail=1 rcpt=1 data=1 quit=1 commands=6
Sep 28 11:58:34 host courier-imaps[23012]: Connection, ip=[::ffff:213.162.73.12]
Sep 28 11:58:34 host courier-imaps[23012]: LOGIN, user=
example@example.at, ip=[::ffff:213.162.73.12], port=[28007], protocol=IMAP
Sep 28 11:58:35 host courier-imaps[23012]: LOGOUT, user=
example@example.at, ip=[::ffff:213.162.73.12], headers=0, body=0, rcvd=447, sent=129, time=1, starttls=1
Sep 28 11:59:04 host postfix/smtp[52321]: connect to gmail-smtp-in.l.google.com[64.233.167.26]:25: Connection timed out
Sep 28 11:59:04 host postfix/smtp[52321]: connect to gmail-smtp-in.l.google.com[2a00:1450:400c:c0a::1a]:25: No route to host
Sep 28 11:59:34 host postfix/smtp[52321]: connect to alt1.gmail-smtp-in.l.google.com[209.85.233.27]:25: Connection timed out
Sep 28 11:59:34 host postfix/smtp[52321]: connect to alt1.gmail-smtp-in.l.google.com[2a00:1450:4010:c03::1b]:25: No route to host
Sep 28 11:59:38 host courier-imaps[23012]: Connection, ip=[::ffff:213.162.73.12]
Sep 28 11:59:39 host courier-imaps[23012]: LOGIN, user=
example@example.at, ip=[::ffff:213.162.73.12], port=[28008], protocol=IMAP
Sep 28 12:00:04 host postfix/smtp[52321]: connect to alt2.gmail-smtp-in.l.google.com[142.250.4.26]:25: Connection timed out
Sep 28 12:00:04 host postfix/smtp[52321]: DC99415145D: to=<
receiver@gmail.com>, relay=none, delay=90, delays=0.31/0.01/90/0, dsn=4.4.1, status=deferred (connect to alt2.gmail-smtp-in.l.google.com[142.250.4.26]:25: Connection timed out)