Sounds like a great way to get more value from old cellphone photos.
Guess the workflow will depend on the quality & resolution of the images you have from your old phones…
For instance, if they were really low res and might be missing some details you might want to experiment with putting the Gigapixel AI into that 1st step because GAI can be helpful intuitively filling in the gaps of missing pixel info in a lot of cases. The point would be to build a more robust starting image before you embark on a more "normal’ post-processing workflow.
You also don’t mention whether you are working in Ps or another host program. Or, strictly Topaz Studio as a standalone product. That could impact your workflow too.
After that GAI application, I personally, would be tempted to run any denoising functionality you prefer. I’m mostly relying on the new DeNoise AI now. But AI Clear, DeNoise 6 or DeHaze can help with cleaning up the image as a good base starting point before you dive into the more “creative” processing options. Essentially you’d be creating a cleaner, sharper image capture simulation with those steps.
For the more creative adjustments and sharpening, then going for the Basic Adjustment and Precision Detail/Precision Contrast can add a bit more personality and potentially restore some texture and structure or dimension to your images (that is if you don’t go too nuts and over-saturate or over-sharpen - a sure sign of over sharpening are little white speckles on your image or the creation of white ‘halos’ around the edges of objects in your images).
If you don’t use a host like Ps CC (which has a camera raw filter option nowadays) then, yes, the jpg to raw program will give you more simulated capability to perform raw adjustments to your image after you denoise. Some of the raw adjustments could be redundant to or duplicative to the adjustments you’d make in “Basic Adjustments”. You’ll have to decide which option works best for which image - but the general rule of thumb is don’t over-process or process more than you have to to achieve the effect you’d like. i.e., If you want to end up with an image that looks like a photo rather than an illustration or digital painting than likely less might be more (either in terms of fewer digital darkroom tools used or a light hand in the tools that are used).