iPad Pro M1 Strage-Manager Feature on the external Monitor/TV doesn't work anymore.

Your monitor’s screen resolution will impact the available settings and external screen capabilities. 

While undocumented, testing has demonstrated that 4:3 monitors with a display resolution of 1280x1024 and below are currently only usable with iPad screen mirroring; as such, associated settings to disable screen mirroring in favour of Stage Manager are not available in iPad Display settings.

When used with a 16:9 widescreen monitor, with a native display resolution of 1920x1080 or greater, the full set of Display settings - and access to Stage Manager - become available.

The iPad User Guide lists the upper resolution limit as 6K - but the Guide offers no lower limit, or suggestion of aspect-ratio, being a factor for compatibility:

Connect iPad to a display with a cable - Apple Support

This discussion thread may be of additional interest:

iPad Extended Desktop not working - Apple Community

In conclusion, your monitor must be capable of 16:9 widescreen 1920x1080 (FHD) to support iPadOS16 Stage Manager extended desktop. Unless the monitor meets the minimum required specifications, you will not see the full range of controls in iPad settings.  However, there have been a few reports of TV/Monitors that should meet the 1920x1080 resolution requirement are failing to work with the current version of Stage Manager.

Whether or not this is an intentional limitation, or a bug introduced with release of iPadOS 16.4.1/16.5, is unknown.

1) As you have a 4K TV, ensure that you are connecting to an HDMI port that supports UHD-4K (as some HDMI ports might only support HD).

2) Ensure that the very last connection made in the connection chain is to the iPad itself. If the initial HDCP handshake that runs when the connection is made fails to detect the TV, you may see strange results.