Mac Mini M4 pro and dual Thunderbolt displays

Yes.

A Mac mini with a M4 Pro chip

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"Simultaneously supports up to three displays:

• Up to three displays: Three displays with up to 6K resolution at 60Hz over Thunderbolt or HDMI
• Up to two displays: One display with up to 6K resolution at 60Hz over Thunderbolt and one display with up to 8K resolution at 60Hz or 4K resolution at 240Hz over Thunderbolt or HDMI"

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If you're talking about the old Apple Thunderbolt Display (27-inch), model A1407, with a resolution of 2560x1440 pixels, you will need an Apple Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter . If your displays have good hydra cables, you can daisy-chain the displays from one adapter. If both have bad or flaky hydra cables - forcing you to use both daisy-chaining ports for Thunderbolt 1/2 "bypass" cables, you will need two adapters.

If you're talking about the modern Apple 27" 5K Retina Studio Display, those come with Thunderbolt 3 cables.

Either way you will be using the Thunderbolt 5 ports on the back of your M4 Pro Mac mini. As far as I know, there is no such thing as a "HDMI (computer) to Thunderbolt (display)" adapter, and these displays want Thunderbolt input. Old-stye Thunderbolt input for the 27" Thunderbolt Display; new-style Thunderbolt input for the 27" 5K Studio one. The USB-C ports on the front of your Mac mini only carry USB – so, like the HDMI port, would not be able to support either type of Thunderbolt Display.

Note: If by any chance, these are not 27" Thunderbolt Displays (model A1407) (whose hydra cables have TWO heads), but 27" LED Cinema Displays (model A1316) (whose hydra cables have THREE heads),

• You will need USB-C (male) to Mini DisplayPort (female) adapters or the equivalent. The Apple TB3-to-TB2 adapter does NOT know how to make its TB2 side look like a "regular" Mini DisplayPort.
• You will still use the Mac mini's Thunderbolt 5 ports (directly, or indirectly, through a dock).
• You will need to connect the USB heads of the hydra cables to your Mac mini, in some way - so that you can adjust the brightness of the monitors.

"Mac Mini M4 pro and dual Thunderbolt displays: Can a new Mac Mini M4 Pro with 10 core CPU and 16 core GPU support dual Apple Thunderbolt displays and would they both connect thru the Thunderbolt 5 ports?"

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Based on personal experience...

Getting 3 External Displays:

The J5 USB-C Dual HDMI Docking Station allows for more than two extra monitors. How so? Well, plug in a display projector the Mac using the USB-C Digital AV Multiport Adapter and then plug the J5 hub with 2 HDMI displays (one 4K), and then you'll have 3 external screens. It all mirrors and extends. It mirror and extends the screens, but not by protocol.

Yes and Yes.