I have a slightly off topic question. Is it a good idea here to be using Office 2010?
Specifically, does Outlook 2010 support proper security authentication methods for accessing e-mail servers today?
Depends on what kind of email server. Office 365, no, because it doesn't support "modern authentication" at all. Exchange 2019, no. POP and IMAP plus SMTP, sure, those still use the same encryption and authentication they always have and probably always will. At some point, SSL/TLS might get updated to a version that Outlook 2010 doesn't support, but that hasn't happened yet, and even after it does, most servers will still allow the older version for many years. (For both O365 and Exchange, technically you can turn on POP/IMAP and SMTP to access a mailbox, if you really really really wanted to pay for an O365 subscription to waste most of the features, or pay thousands of dollars for an Exchange server and not use its features. Or had one specific need for POP/IMAP in addition to using the full feature set.)
If you're using Outlook and not using an Exchange server or O365, you're using either POP or IMAP, with IMAP being the most common these days when you let the client auto-detect settings. GMail, iCloud Mail, and everything else uses POP/IMAP and SMTP when you connect with a general email client rather than a dedicated branded client like the GMail app (which uses https to transfer the data to the local database).
The question of whether it's a good idea is very different. The authentication and encryption for accessing those servers is the same regardless of the version of Outlook you use. The only issue that might arise in regards to the authentication and encryption itself would be in regards to SSL and TLS flaws. Since Outlook isn't being updated, if flaws are discovered in one of those, the remote servers and other apps that use SSL/TLS like your web browser or newer versions of Outlook would get updated when the flaws are fixed. Outlook would still be able to connect for years using its flawed version because the servers probably wouldn't quickly cut off users of the flawed version, but it would be a vulnerable connection.
What matters more is whether the particular implementation and the app overall has security flaws and vulnerabilities. There probably isn't much difference in the code for the different versions of Outlook in regards to POP/IMAP and SMTP access, but there is a lot of surrounding code that IS different, and since Office 2010 hasn't gotten security updates for years, there is a greater risk of flaws and vulnerabilities being found and exploited which won't ever get patched by Microsoft. So that just comes down to "using old and unsupported software is a security risk, even if you don't know of any problems right this minute".
