If Pageant has already loaded keys, then you can make a use of it by another application through the Plink (PuTTY Link) command-line interface.
If you want to work with e.g. a Git repository on remote server with credentials (keys), I have found a working solution:
https://www.cgranade.com/blog/2016/06/06/ssh-keys-in-vscode.html (with already loaded keys to Pageant, the only missing part is last step 4).
You need to set a new environment variable in your Win10.
For me it worked when I added a "system variable" not a "user variable".
The name of the variable is:
"GIT_SSH"
The value is a full path to PuTTY\plink.exe, e.g:
"C:\Program Files (x86)\PuTTY\plink.exe"
If you have VS Code opened already, close it and reopen again to make sure it sees the new environment variable.
Update (2021.11.10):
Now in my case, VSCode additionally needed what was described here in the solution:
VS Code / Bitbucket / SSH - Permission denied (publickey)