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The error you're seeing is due to a threading issue—Visual Studio is trying to update the Output window from a background thread to fix that please follow below step by step process for better understand
Run Visual Studio as Administrator – Right-click the shortcut and select “Run as administrator”.
- Update Visual Studio & SSDT – Ensure both Visual Studio 2022 and SQL Server Data Tools are fully updated. Get error deploying to analysis services via VS 2022 Community to SQL 2019 - Microsoft Q&A
- Check Compatibility – Confirm the tabular model is compatible with SQL Server 2019 SSAS.
- Reset Output Window – Go to (view > output) and ensure it’s properly configured.
- Rebuild Project – Clean and rebuild before deploying.
- Reset VS Settings – Use (Tools > Import and Export settings > Reset all settings) if needed.