The proper email programs have an option somewhere in the settings to either store a copy of the mailbox on the computer, or not do it. I’m pretty sure that’s in Thunderbird, Evolution, etc. I’m not sure about Outlook.

If you have access to some sort of basic Linux system (cloud server, local server whatever works for you) you can run a program on a timer such as https://isync.sourceforge.io/ (Debian package: isync) which reads email from one source and clones it to another. Be careful and run it in a security context that meets your needs (I use a local laptop w/encryption at home that runs headless 24/7, think raspberry Pi mode).

This includes IMAP (1) -> IMAP (2) as well as IMAP -> Local and so on; as with any app you’ll need to spend a bit learning how to build the optimum config file for your needs, but once you get it going it’s truly a “set and forget” little widget. Use an on-fail service like https://healthchecks.io in your wrapper script to get notified on error, then go about your life.

Edit: @[email protected] glanced at your comments and see you have a lot of self-hosting chops, here’s a markdown doc of mine to use isync to clone one IMAP provider (domain1.com) to another IMAP provider (domain2.com) subfolder for archiving. (using a subfolder allows you to go both ways and use both domains normally)

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Sync email via IMAP from host1/domain1 to a subfolder on host2/domain2 via a cron/timer. Can be reversed as well, just update Patterns to exclude the subfolders from being cross-replicated (looped).

• Install the isync package: apt-get update && apt-get install isync

Passwords for IMAP must be left on disk in plain text

• Generate “app passwords” at the email providers, host1 can be READ only
• Keep ${HOME}/.secure contents on encrypted volume unlocked manually

The mbsync program keeps it’s transient index files in ${HOME}/.mbsync/ with one per IMAP folder; these are used to keep track of what it’s already synced. Should something break it may be necessary to delete one of these files to force a resync.

By design, mbsync will not delete a destination folder if it’s not empty first; this means if you delete a folder and all emails on the source in one step, a sync will break with an error/warning. Instead, delete all emails in the folder first, sync those deletions, then delete the empty folder on the source and sync again. See: https://sourceforge.net/p/isync/mailman/isync-devel/thread/f278216b-f1db-32be-fef2-ccaeea912524%40ojkastl.de/#msg37237271

Simple crontab to run the script:

0 */6 * * * /home/USER/bin/hasync.sh

Main config for the mbsync program:

${HOME}/.mbsyncrc

# Source
IMAPAccount imap-src-account
Host imap.host1.com
Port 993
User user1
PassCmd "cat /home/USER/.secure/psrc"
SSLType IMAPS
SystemCertificates yes
PipeLineDepth 1
#CertificateFile /etc/ssl/certs/ca-certificates.crt

# Dest
IMAPAccount imap-dest-account
Host imap.host2.com
Port 993
User user2
PassCmd "cat /home/USER/.secure/pdst"
SSLType IMAPS
SystemCertificates yes
PipeLineDepth 1
#CertificateFile /etc/ssl/certs/ca-certificates.crt

# Source map
IMAPStore imap-src
Account imap-src-account

# Dest map
IMAPStore imap-dest
Account imap-dest-account

# Transfer options
Channel hasync
Far :imap-src:
Near :imap-dest:HASync/
Sync Pull
Create Near
Remove Near
Expunge Near
Patterns *
CopyArrivalDate yes

This script leverages healthchecks.io to alert on failure; replace XXXXX with the UUID of your monitor URL.

${HOME}/bin/hasync.sh

#!/bin/bash

# vars
LOGDIR="${HOME}/log"
TIMESTAMP=$(date +%Y-%m-%d_%H%M)
LOGFILE="${LOGDIR}/mbsync_${TIMESTAMP}.log"
HCPING="https://hc-ping.com/XXXXXXXXXXXXXXXXXXXXXXXXX"

# preflight
if [[ ! -d "${LOGDIR}" ]]; then
  mkdir -p "${LOGDIR}"
fi

# sync
echo -e "\nBEGIN $(date +%Y-%m-%d_%H%M)\n" >> "${LOGFILE}"
/usr/bin/mbsync -c ${HOME}/.mbsyncrc -V hasync 1>>"${LOGFILE}" 2>&1
EC=$?
echo -e "\nEC: ${EC}" >> "${LOGFILE}"
echo -e "\nEND $(date +%Y-%m-%d_%H%M)\n" >> "${LOGFILE}"

# report
if [[ $EC -eq 0 ]]; then
  curl -fsS -m 10 --retry 5 -o /dev/null "${HCPING}"
  find "${LOGDIR}" -type f -mtime +30 -delete
fi

exit $EC

For historic emails, you could setup a forwarding rule from the primary to the backup. This would need to be done in advance of course