It really depends on the consistency of the photos and maybe more importantly, the colour of the subject. PS has the ability to do selections on colour range, so you record your actions on processing a single image to create a PS Action that you can then apply to other images.
If this works, then you can apply the action in a batch process against all your images and let it run.
If your images don't allow for the easy color range selection though, you won't be able to automate it like this. Manually doing the selection will be very time consuming.
Answer from Robin on Stack ExchangeAutomate change background to white on all images? - Photography Stack Exchange
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Looking to change the background of a photo on my iPhone. People suggested that I use a photo background remover app or online tool to remove the background of the photo first and then add a new background to it. Recommend me if there is an app or an online tool that I can use. Or whether the iPhone, especially iOS17 or iOS 18 lets you do this natively or not?
You haven't talked about your lighting at all, but that's almost definitely where the problem is. Simply, the background needs to be lit independently of the foreground. You almost definitely need more space between subject and background (to avoid light spill) and depending upon subject size you may need several lights to evenly light the background adequately. Meter for the background and subject independently so that you can be sure enough power is being put out on the background to make it white.
Another problem -- though much smaller -- is likely that using the ColorChecker is working against you. The background is almost definitely not a brilliant pure white, so the color adjustments you're making are helping to bring that down to a more realistic almost-white. Again, lighting the background independently of the foreground helps solve this because you can be sure you're setting the flash output on the background to something that will ensure white is... white.
If the white balance and white point are correct, then the background should be displayed as white. If it isn't, then you are doing something wrong with your color target. If it is a good neutral grey, then the white balance is correct, but the white point is too bright. I would adjust the white point to bring the white point up to where it belongs.
It may also mean that you don't have enough light on the background if the subject has brighter highlights than the background itself (in which case it isn't going to be possible to get a white background without selective color replacement or matte painting). If the subject is more brightly lit than the background, then relatively speaking, the background would be grey.
If the background was too dark and the subject is too bright to bring up the white point overall, then you will need to mask out the subject so you can work exclusively on the background. If it's a fairly regular color, you can probably use the magic select to get a quick starting point. Once you have a mask for the background, you can apply an exposure correction or simply change the color of the background by itself.