@Mariekevsch To add to what @JohannesLindner said...
Modify tools in ArcGIS Pro that work on selected features have a built in select tool called the Active Select tool:
...that as you found out, honors the current selection combination mode. If you keep the selection mode as the default (Create a new selection), you can add to the selection by holding SHIFT and then clicking on another feature.
With Modify tools, it's a best practice to use the Active Select tool on the pane instead of the core Select tool found on the ribbon. Both will work to make selections, but the Active Select tool does some additional work of automatically filtering the selection to a subset of features that are editable and work with the current tool. Then once a valid selection exists, the modify tool becomes the active tool (unlike the core select tool, which will select anything that is selectable and will not automatically enable the modify tool).
More on selecting features for editing - https://pro.arcgis.com/en/pro-app/latest/help/editing/select-features-for-editing.htm
Another tip that I will add: if you use the Move tool frequently, you can add it to the Quick Access Toolbar so it will be available to you without having to switch to the Editing ribbon:
More on the QAT: https://pro.arcgis.com/en/pro-app/latest/get-started/quick-access-toolbar.htm
-Scott