Safelinks is one of the features of Microsoft’s Advanced Threat Protection (ATP) system on their mail servers. Microsoft handholds their users by modifying hyperlinks in e-mails to redirect to their own server, have it check its blacklist to determine the target is untoward, and then commits the redirection to the original target if the target is considered safe.
Safelinks is not available if free MS accounts. If you have, or ever had, an MS 365 (aka MS Office) account, ATP was enabled by default. I had an MS 365 account for 3 years, but dropped their subscriptionware, but the Safelinks feature was still enabled in my Hotmail and Outlook.com accounts. When I had the paid MS 365 service, supposedly there was a security → advanced setting to disable it. I didn’t notice the rewritten hyperlinks until after I dropped MA 365, had a free account, and the setting to disable Safelinks was not available for my free account. I had to use the feedback link in their webmail client to request they disable the Safelinks “feature” in my account.
Besides chaining hyperlinks to their server (adding more links which makes the navigation more fragile, and causes link rot should they ever discontinue their redirection service), I used to report spam. However, parsing the body of the e-mail on spam had the URLs pointing to my own e-mail provider (Microsoft) because they were redirection URLs (point to MS server with an argument in the URL pointing to the original URL).
If you have a paid MS account, there might be a security option to let you disable Safelinks. You have to login into your account to change the setting up on the server. If you have a free MS account now, you have to use their webmail’s feedback to ask them to disable Safelinks.
E-mail is still probably the number one infiltration vector for malware. Microsoft added ATP/Safelinks to handhold their users that were foolish in blindly clicking on hyperlinks in e-mails, or not bothering to check to where they pointed although most e-mail clients will show a popup when hovering over a hyperlink to show its target (however, there are still some tricks, like using Punycode, to obfuscate the destination). For some users, Safelinks is added protection. For some users, it is a pain in the arse. If Microsoft ever drops their ATP service, or their ATP server is down, or their ATP server is unreachable at the time you click on their redirection URL, the redirection URL won’t work since the redirection server is unusable.
Some users have web browsers, or configured them, or installed add-ons that interpose on redirection. So, it’s possible your web client or its add-ons are blocking the Safelink redirections.