Any error in your JavaScript console?

What is the content of https://<hostname>/SOGo/so/<username>/Mail/0/view ?

While loading this URL, sniff the IMAP traffic and check for the server's response to the getquotaroot command.

No error in JavaScript console

The URL is not valid:
https://<hostname>/SOGo/so/<username>/Mail/0/view [^]
the called object returned no result

I've compared Dovecot debug-log login with Roundcube and SOGo and there is no difference.

Enabling ImapDebugEnabled in SOGo I can see following:

sogod[32539]: S[0x556a69e16030]: 1 OK [CAPABILITY IMAP4rev1 SASL-IR LOGIN-REFERRALS ID ENABLE IDLE SORT SORT=DISPLAY THREAD=REFERENCES THREAD=REFS THREAD=ORDEREDSUBJECT MULTIAPPEND URL-PARTIAL CATENATE UNSELECT CHILDREN NAMESPACE UIDPLUS LIST-EXTENDED I18NLEVEL=1 CONDSTORE QRESYNC ESEARCH ESORT SEARCHRES WITHIN CONTEXT=SEARCH LIST-STATUS BINARY MOVE LITERAL+ NOTIFY QUOTA] Logged in
sogod[32539]: S[0x556a69e16030]: CAPABILITY IMAP4rev1 SASL-IR LOGIN-REFERRALS ID ENABLE IDLE SORT SORT=DISPLAY THREAD=REFERENCES THREAD=REFS THREAD=ORDEREDSUBJECT MULTIAPPEND URL-PARTIAL CATENATE UNSELECT CHILDREN NAMESPACE UIDPLUS LIST-EXTENDED I18NLEVEL=1 CONDSTORE QRESYNC ESEARCH ESORT SEARCHRES WITHIN CONTEXT=SEARCH LIST-STATUS BINARY MOVE LITERAL+ NOTIFY QUOTA
sogod[32539]: S[0x556a69e16030]: 2 OK Capability completed (0.001 + 0.043 + 0.042 secs).
...
...
...
sogod[32539]: S[0x556a69e16030]: 6 OK List completed (0.001 + 0.042 + 0.042 secs).
sogod[32539]: C[0x556a69d81540]: 7 getquotaroot "INBOX"
sogod[32539]: S[0x556a69e16030]: QUOTAROOT INBOX "User quota"
sogod[32539]: S[0x556a69e16030]: * QUOTA "User quota" (STORAGE 338146 2097152)
sogod[32539]: S[0x556a69e16030]: 7 OK Getquotaroot completed (0.009 + 0.000 + 0.008 secs).

It looks like SOGo is able to read quota, but not showing up in the UI

Fixed in SOPE.

See https://github.com/inverse-inc/sope/commit/0f5d66fabe9232ef0f03f15670103a69ffede35e