Increasing the timeout is worth a try. However, I don't have high hopes that it will solve the problem. The reason is that the timeout configuration is something implemented in the Arduino IDE application (or to be more precise, in its Arduino CLI helper tool). The error you encountered is caused by the connection being closed by the remote host, not locally. The timeout configuration doesn't have any effect on the remote host.
Also worth mentioning is that the bug that caused the timeout mechanism to spuriously terminate healthy downloads over a slow Internet connection was fixed in Arduino IDE 2.3.8:
So the default timeout configuration will now be suitable for the vast majority of users, and should only ever terminate a download when something is clearly wrong. It is likely that a custom timeout would now only be used by advanced users in niche cases (most likely automated applications instead of manually working with Arduino IDE) where they want the download to be terminated more quickly in the event of a problem instead of waiting for the long default timeout to trigger.
Great work finding a workaround for the problem. This indicates that the cause of the problem is something with your normal network/Internet connection (as opposed to a problem with the Arduino IDE application).
Do you access the Internet through a proxy or VPN? The use of proxy servers is common in institutional networks at workplaces.