Leaving S mode is free but permanent. On the PC, go to Settings > System > Activation, find the option to switch out of S mode, select Go to Store, and on the “Switch out of S mode” page select Get. Do not choose the Windows Pro upgrade option unless you actually want to purchase Pro. Once you leave S mode, you cannot enable it again.
For the remote connection, it is important to clarify what you want to do. If you only want to connect from this PC to another computer, Windows 11 Home can do that using Remote Desktop Connection. However, if you want other computers to connect remotely to this PC, Windows 11 Home cannot act as a Remote Desktop host; Microsoft requires Windows 11 Pro or another supported Pro edition for that.