I do not mean to be rude, but I will be flat honest. Your expectations are unreal.

even the tiniest micro details to show

What is micro for you? Most of the texture you see at a "magnifying glass" level is given by the paper, for example, a cotton based paper is almost impossible to print because of the roughness is specially made to receive pigments in watery form.

The oily sensation an oil-based paint has volume has a glossy reflectiveness only oil paint can give.

You chose a medium for paint because of the materials of the paint.

Almost any reproduction system is based on a limited amount of inks screened in some way to simulate gradients. That is the difference between continuous tone and halftone.

Would I use offset printing or digital?

... ! ... Do you need one? or one thousand? That is the parameter to decide Digital vs Offset.

Process or spot colors?

... ! ... This discards digital all together... Is your paint monochromatic? go for a Pantone... if it is not...

Specially made ink?

Does your painting have a strange finish unreproducible by a standard printing system?

I do not know what you want for an ink... You can use chocolate muse if you want... but you could need silkscreen for this.

I want the colors to be as similar as possible

If this is a real question...

Use a color calibrated workflow.

1. Light with good CRI index.

2. Use a color chart for reference.

3. Chose a good lighting technique.

4. Get a good camera and lens. There are some other posts on the forum about this.

5. Calibrate your editing software with the profile you have with point (2)

6. Use a good quality printer, probably inkjet-based.