There will likely be an unpredictably large amount of other issues (character encoding, date formatting, etc.) that you'll have to work through.
The way I might approach this problem is, if the tables are exactly identical, or you didn't make any changes within power query (like removing columns, merging tables, etc.) you may be able to modify the M code within the advanced editor, and try to swap the data sources to see if it works.
Go into "Transform Data"
Select the table you want to modify
Click the "Advanced Editor" icon in the ribbon.
Here, I imported an excel file, but for you, it should show some kind of "AnalysisServices" line. I don't have an SSAS database to connect to so I can't validate. Try replacing this line with the connection string to your SSAS datasource and see if it works.
Save, apply update, and see if it works?
Again, this is not really advisable, but if you want to give it a try, and the data sources are identical, this is how I might approach the problem before just re-making the report whole-cloth.