Demo should be long completed. It's messy and needs to be all done at one time. You are also not factoring any floor prep, which will be needed, and is often quite significant.

I wouldn't count on old cabinets being worth saving and painting. The old stapled drawers with epoxy side mount glides will tell you to buy new. Also, all cabinets need to be set at the finished floor height. Or you will have issues with appliances and clearances. With you doing new flooring, that can be a big issue, unless you are doing a thin vinyl.

Cabinets also need to be perfectly level in all 6 dimensions, in order to provide the correct substrate for the counters. Old cabinets can have a problem with that and may need shimming, or even rebuilding, or removing and reinstalling.

I figured floor prep would be included when we put down the new tile. The cabinets are of great quality and are in good condition. The only problem is the wood grain is such an outdated color. We actually stained the cabinetry in 3 other places in the house. However, that was a really dark chocolate and we would like to lighten up the kitchen more. So we are going to try painting.

Will the floor level change when you retile? Will the tile run under the appliances? I assume the tile won't run under the cabinets as you are not replacing them. Just make sure you don't create an issue with appliances you can't slide out because the flooring is not the same height so they are essentially tiled in, or with appliance height vs cabinet height vs counter height - you need to consider all these specifics to make sure the new flooring will allow your kitchen to function correctly.

Oh and consider changing out cabinet hardware for a new refreshed look, if needed. Good luck!

I know the tile runs under the refrigerator and the range. I'd have to go check on the dishwasher. If it changes, it will be minimal

As mentioned earlier the cabinets will need to be leveled for any type of countertop. Laminate countertops will conform to unlevel cabinets, any hard surface will not. The countertop folks will simply shim their countertop level leaving unsightly gaps, because cabinetry leveling is not in their job description. Once you put new countertops on old cabinets using hard surfaces such as granite or quartz. you are stuck with those cabinets forever as no one will remove those countertops and attempt to install them over new cabinets due to the chance of them breaking.