@Katt I am not a Photoshop expert, but I'll try my best to share what works for me with Procreate since you may be more comfortable with it. I tried to do a quick edit for your grey whale art to help you visualise what I mean.
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My first step is to scan the painting at 400-600dpi. The reason is that sometimes we have to edit at pixel level and it is going to look quite rough especially on the edges. Working on a higher dpi helps to make the end result look more natural
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Second step is look at your raw scan and identify what you don't like about it and what you like and wish to keep. In the grey whale case, I don't like: the yellowish cast from the scan, the colour of the sea that doesn't help the whale stand out. I like: the splashed paint colours and texture
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list item Open in Procreate. Duplicate it. Hide the original and work on the duplicate so in case your edits don't turn out good, you still have the original to start over
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list item Auto-select the white background, slide until you get a good coverage that removes most of the paper white without touching any of the whale or splatter. Don't worry if there are bits of white left, you can always use a small eraser to remove these bits. Zoom in a lot to erase around the fine splatter marks. I erased the water texture too because they don't seem to scan well and there is no way for me to fix it quickly. I will put back the water digitally later.
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list item Add a new layer underneath. I do a rectangular selection and paint within the selection with a flat brush, followed by a "Bonobo" chalk brush to add the texture. Finally, add some of the white wave crests with "Artist Crayon" brush. Both are available in Procreate Default.
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list item It may be worth trying to paint the background separately and then layer them together digitally if you want both background and character to keep the 100% traditional feel.
I hope you'll give it a try and let me know if it works for you!