To Publish ImageServer with Imaging service from ArcPro, you don't need to connect ArcPro with ArcGis server. The old way use ArcMap then you do need create a server connection from ArcCatalog. Then right click server, publish image service.
However with ArcPro, if you want to publish the TIF image as an image service(stand alone ImageServer),
Right-click on the TIF image on the Catalog pane > Share as web layer > Imagery.
If you need to publish a mosaic dataset as an image service, we would need an ArcGIS Image server license.
Let's check the result
https://transparentgov.net:3200/googlemaps910/default?layer=community%2FPalmSpringsNoise2020ImageServer¢er_lat=33.860804934364275¢er_long=-116.46897758110613¢er_zoom=14&url=https%3A%2F%2Fgisnexus.palmspringsca.gov%2Fserver%2Frest%2Fservices%2Fcommunity%2FPalmSpringsNoise2020ImageServer%2FImageServer&overlayType=overlayType_image&panto=0
https://transparentgov.net/json2tree/esri/server/folder.html?org=https%3A%2F%2Fgisnexus.palmspringsca.gov%2Fserver%2Frest%2Fservices&url=https%3A%2F%2Fgisnexus.palmspringsca.gov%2Fserver%2Frest%2Fservices&arcgis_online_token=&select_folder=50&select_layer=-1
ESRI map e101
https://transparentgov.net:3200/googlemaps910/default?layer=community%2FPalmSpringsNoise2020ImageServer¢er_lat=33.77221617439925¢er_long=-116.56393767799436¢er_zoom=11&url=https%3A%2F%2Fgisnexus.palmspringsca.gov%2Fserver%2Frest%2Fservices%2Fcommunity%2FPalmSpringsNoise2020ImageServer%2FImageServer&overlayType=overlayType_image&panto=0