After replacing the A/C compressor now engine bogs down when the A/C is on

It is not uncommon for an engine to bog down when the compressor comes on especially these smaller 4 cylinder engines. However, if this is noticeably different then the likely cause of this is a faulty compressor.

Basically the compressor is slightly locked up which means when the clutch engages it actually slows the engine down.

I would suggest contacting the company that sold it to you or installed this and have them inspect it.

https://www.2carpros.com/articles/replace-air-conditioner-compressor

Also, what do the RPMs drop to when this happens? Does it only do this when idling or while you are driving as well? Do you notice a lack of power?

https://www.2carpros.com/articles/symptoms-of-low-engine-power

Maybe if you get a video of this, that will help with getting us on the same page. Thanks