[exim] exim4 stopped sending mail after upgrade from Debian/…

I've done some testing using smtp-cli and it seems to work. I never get
the e-mail, but it seems to have succeeded to making the connection...
Here's the session, starting with the command and including entire
output (only my customer's domain name has been removed)

smtp-cli --verbose --host=web71.dnchosting.com --enable-auth --user
sendmail@<one of my domains> --from sendmail@<one of my domains> --to
gary@??? --data /etc/exim4/test.text

Enter password for sendmail@<one of my domains>@web71.dnchosting.com :
Connection from 192.168.1.17:50520 to 192.64.150.71:25
[220] 'web71.dnchosting.com ESMTP Exim 4.94.2 #2 Sun, 22 Aug 2021
16:18:30 -0400 '
[220] 'We do not authorize the use of this system to transport
unsolicited, '
[220] 'and/or bulk e-mail.'
> EHLO localhost
[250] 'web71.dnchosting.com Hello
cpe0018e7d3134a-cmf81d0f8158d0.cpe.net.cable.rogers.com [99.248.170.28]'
[250] 'SIZE 52428800'
[250] '8BITMIME'
[250] 'PIPELINING'
[250] 'PIPE_CONNECT'
[250] 'AUTH PLAIN LOGIN'
[250] 'STARTTLS'
[250] 'HELP'
Starting TLS...
> STARTTLS
[220] 'TLS go ahead'
Using cipher: ECDHE-RSA-AES128-GCM-SHA256
Subject Name: /CN=web71.dnchosting.com
Issuer  Name: /C=US/ST=TX/L=Houston/O=cPanel, Inc./CN=cPanel, Inc.
Certification Authority
> EHLO localhost
[250] 'web71.dnchosting.com Hello
cpe0018e7d3134a-cmf81d0f8158d0.cpe.net.cable.rogers.com [99.248.170.28]'
[250] 'SIZE 52428800'
[250] '8BITMIME'
[250] 'PIPELINING'
[250] 'PIPE_CONNECT'
[250] 'AUTH PLAIN LOGIN'
[250] 'HELP'
AUTH method (PLAIN LOGIN): using LOGIN
> AUTH LOGIN
[334] 'VXNlcm5hbWU6'
> c2VuZG1haWxAcm9zc2xhbmQuZGVudGFs
[334] 'UGFzc3dvcmQ6'
> VGVycmlibGUyc2hvVXNl
[235] 'Authentication succeeded'
Authentication of sendmail@<one of my domains>@web71.dnchosting.com
succeeded
> MAIL FROM:<sendmail@<one of my domains>>
[250] 'OK'
> RCPT TO:<gary@???>
[250] 'Accepted'
> DATA
[354] 'Enter message, ending with "." on a line by itself'
[250] 'OK id=1mHtvL-0001x5-4I'
> QUIT
[221] 'web71.dnchosting.com closing connection'


When I send e-mail through exim4, it simply stays in the queue. I'm not
seeing any error messages in the exim4 log (/var/log/exim4/mainlog)
other than ones saying the mail is still in the queue (retry limit not
reached).

I have another (working) server (in a different location) that I also
upgraded a few days earlier with identical (AFAICT) Debian configuration
except for some names & passwords (different smarthost and accounts with
a different hosting company). When I try using those names instead, it
still doesn't work. Yet this other server is sending me e-mail just the
way it always did.

Clearly there is a difference in the two setups but I can't see it.
smtp-cli was my attempt to debug the problem but since it seems to be
working, I'm stumped. Can anyone suggest something I can try to find the
problem?