[MCL-21123] Launcher is unable to contact api.minecraftservices.com on Win 7 due to TLS issue

Windows 7 x64

Win32 launcher 2.2.10327

Minecraft Java, Microsoft account

The MC launcher is unable to connect to the Minecraft servers:

Clicking 'Try again' obviously does nothing.

This is not an account issue, I can access my Minecraft account through Minecraft.net in a browser without issue.
It's not a network connectivity issue, everything else works fine. I do not have any kind of VPN or firewall that is blocking network traffic.
It's not a temporary issue, it's been broken for some time (maybe 12 - 24 hours).
This configuration has worked for a long time and suddenly stopped without any change on my end.

The launcher_log.txt has numerous lines like this:

[Info: 2022-02-10 20:24:28.7595728: NetQueue.cpp(588)] NetQueue: Starting net action https://api.minecraftservices.com/launcher/login
[Info: 2022-02-10 20:24:28.8325728: NetQueue.cpp(429)] NetQueue: Primary ip: 52.85.193.117, Host: api.minecraftservices.com
[Info: 2022-02-10 20:24:28.8325728: NetQueue.cpp(467)] NetQueue: Action failed with result "schannel: next InitializeSecurityContext failed: SEC_E_ILLEGAL_MESSAGE (0x80090326) - This error usually occurs when a fatal SSL/TLS alert is received (e.g. handshake failed). More detail may be available in the Windows System event log." (35) : https://api.minecraftservices.com/launcher/login
[Info: 2022-02-10 20:24:28.8325728: NetQueue.cpp(507)] NetQueue: Action finished: https://api.minecraftservices.com/launcher/login
[Error: 2022-02-10 20:24:28.8325728: Common_p.h(122)] Error while sending request to https://api.minecraftservices.com/launcher/login
[Error: 2022-02-10 20:24:28.8325728: Common_p.h(153)] Unexpected error while making POST request to https://api.minecraftservices.com/launcher/login: Error: schannel: next InitializeSecurityContext failed: SEC_E_ILLEGAL_MESSAGE (0x80090326) - This error usually occurs when a fatal SSL/TLS alert is received (e.g. handshake failed). More detail may be available in the Windows System event log.
[Info: 2022-02-10 20:24:28.8325728: NetQueue.cpp(530)] NetQueue: Action failed in finalization: https://api.minecraftservices.com/launcher/login
[Warning: 2022-02-10 20:24:28.8325728: UserIdentity.cpp(457)] Failed to refresh entitlements. Error: 16

This indicates that the launcher can't make a TLS connection to api.minecraftservices.com, most likely due to a certificate issue. If I had to guess, this is a Windows 7 issue because Win7 has problems supporting newer SSL/TLS features. (Though I have no idea why the launcher is using the operating system for making https requests, that seems like something it should do itself.) I can access https://api.minecraftservices.com/ without issue in a browser (although it's a blank page, as expected; but no TLS connection error) which conclusively rules out a network issue and points to a Win7+TLS cert issue.

The errors mention the Windows Event Logs, which I have checked and there are no messages of relevance corresponding to the timestamps in the logs.