If someone else comes along this Question. The answer to this has been given by Matija Nalis in the P.S. section.

You have to use http://localhost:8080/tiles/... in your URL instead of http://localhost:8080/tms/...

It is also described in the Mapproxy-doc: https://mapproxy.org/docs/latest/services.html#google-maps

The TMS standard counts tiles starting from the lower left corner of the tile grid, while Google Maps and compatible services start at the upper left corner. The /tiles service accepts an origin parameter that flips the y-axis accordingly. You can set it to either sw (south-west), the default, or to nw (north-west), required for Google Maps.

Example: http://localhost:8080/tiles/osm_EPSG900913/1/0/1.png?origin=nw

If someone else comes along this Question. The answer to this has been given by Matija Nalis in the P.S. section at the bottom of their answer.

You have to use http://localhost:8080/tiles/... in your URL instead of http://localhost:8080/tms/...

It is also described in the Mapproxy-doc: https://mapproxy.org/docs/latest/services.html#google-maps

The TMS standard counts tiles starting from the lower left corner of the tile grid, while Google Maps and compatible services start at the upper left corner. The /tiles service accepts an origin parameter that flips the y-axis accordingly. You can set it to either sw (south-west), the default, or to nw (north-west), required for Google Maps.

Example: http://localhost:8080/tiles/osm_EPSG900913/1/0/1.png?origin=nw