Best tool & approach for batch 'refreshr of large quantity of old scans and photos

It's not my area of expertise, and as the other p[oster with the strange name has mentioned, the colour casts were quite different in your two examples.  This one is now 4098 x 2929 pixels, and cleaned up both with Topaz Photo Ai, but it took three Adjustment layers to get the color this far.  Like I said... not my thing.

You could try making them B&W and using the Neural Filter > Colorize, but it did a pants job on thisa one.

There will be tutorials out there on how to fix scanned colour negs, but I am not sure how well they will work.

@erick_7263 My first thought was an action. But every image has different lighting, shadows, and color casts. While a simple action can apply the same steps to everything, it won't adapt to each photo's unique needs. I think you may need to combine both apps. For the images that have visible dust, scratches, or need superior upscaling, send them from Lightroom to Photoshop for the more intensive, targeted, and often manual repair work. On the flip side, Lightroom's powerful batching allows you to apply "Auto" to one image, then select many similar images and "Sync" the settings. This is where you'd tackle the brown/yellow tints. and white balance corrections on groups of similar images.