Answer: A and C

I didn't get this condition  cq: lastReplicated!=  completely?   What is your complete requirement to start the workflow?

Please do share workflow launcher configuration if it is possible.

I would like to ask couple of questions here -   1. How are you starting workflow on huge number of pages? 2. Did you monitor replication queues during publish? 3. Have you used any query in your workflow code? Could you please share the logic, if it is possible.

Could you please share the screenshot of user's permissions tab, it will help me to debug.

I feel if you add those users to OOTB content-authors user group as shown below then they will be able to use pick button as expected -     I have tested at my end. Please give a try. 

Is there specific reason you want to use both Classic and Touch UI while authoring? Just wanted to understand authoring challenges here.

What is the functional significance of private folder [path: /content/dam/private/time-management.jpeg]. I have seen in your logger statement.

While uploading asset via AEM Desktop app I am seeing INFO below - 05.02.2023 17:59:53.436 *INFO* [127.0.0.1 [1675600193357] HEAD /api/assets/we-retail/en/people/mens/aem-gems-012016-oak-lucene-indexes-async-local.pdf.json HTTP/1.1] org.apache.sling.engine.impl.SlingRequestProcessorImpl service: Res...

I have tested with local AEM 6.5.14 and able to upload assets into DAM using desktop app - Could you please check whether you are able to upload assets first. Then try to impersonate as client and give a try to upload assets via AEM Desk Top app.