[autocomplete] InputProps startAdornment incompatibility with multiple #22103

• The issue is present in the latest release.
• I have searched the issues of this repository and believe that this is not a duplicate.

Current Behavior 😯

Within lab version 4.0.0-alpha.56, core 4.11.0, when you use startAdornment within InputProps in Autocomplete, as well as multiple. The multiple tags do not appear but act as though you triggered them.

Expected Behavior 🤔

Have a startAdornment persisting at the same time as using multiple tags

Steps to Reproduce 🕹

Proof can be found here
Within said demo you will see 2 autocomplete fields, the only difference (besides the ID) is that the top (broken) one sets the startAdornment to "test", whilst the second does not.
Plain code can also be found here incase for some reason the sandbox doesn't work.

Steps:

1. Setup a autocomplete
2. Setup renderInput
3. RenderInput uses TextField
4. TextField sets InputProps
5. InputProps sets startAdornment (whether it is text or icon doesn't matter)

Context 🔦

Attempting to use the startAdornment as a "pending" kind of tag. So the user first uses AC to figure out what "tag" then when that is done, it is passed to startAdornment, and based upon that, the user is then prompted with AC based upon said "tag".

Your Environment 🌎