There is something weird going on in your installation. Are you sure you are using 180.7? Are you sure it is a "clean" use of a portable build, that is, nothing unusual like copying only some of the files from the 180.7 unzipped hierarchy and then pasting them elsewhere?
Let's walk through this together step by step:
Here's what I did: Using 180.7 in Windows 11 (feel like I'm declaring namespaces when I write that... :-), I downloaded the ne_10m_admin_1_states_provinces shapefile from Natural Earth and imported that, to get a table with lots of fields, some of them numbers and some of them nvarchar text. I then opened the table and using Edit - Schema added a Unique_ID field of type nvarchar to the table.
With the focus on the opened table window, I opened the Transform pane.
As noted in the Transform Pane topic, using the Transform pane is a two-step process:
Step 2: At the top level you pick the layer you want to work with and the field within that layer you want to operate on. The pane then updates the list of possible templates to those which work with the data type of the field you picked. For example, it doesn't show "Arithmetic" if you picked a field that is nvarchar text.
Step 2: You pick the template you want to use and the Transform pane goes a level deeper into that template. Many of the templates also have Field boxes to allow picking some other field. The lists in those Field boxes will only show fields with data types that are the same as the initial field you picked. For example, if you picked a numeric field and then picked the Arithmetic template, the Field box in the Arithmetic template isn't going to list nvarchar text fields.
In all cases of the Field box, the lists in the Transform pane's Field box show fields in alphabetical order, not in the order they're displayed in the Layers pane.
I had no problem in step 1 clicking the Field box at the top level Transform pane and then pressing 'u' on the Keyboard. It instantly picked Unique_ID as the field, and then correctly refreshed the template list to show only templates that work with nvarchar text types.
If I clicked into any of those templates, such as 'Concatenate', the Field box in the template correctly showed only text type fields.
Likewise, if at the top level I chose any field that is a numeric type, the template list instantly refreshed to show only templates that work on numbers. If I chose one of them, like 'Arithmetic', the Field box in the template correctly showed only numeric types.
I tried to duplicate your "picker" screenshot. That shows a template list for numbers, so the AR... you had picked (or maybe it was the first in your list) has to be a numeric type. I picked a numeric type, mapcolor13, to get the numeric template list. I then clicked in the Field box again, pressed 'u' on the keyboard, and it instantly loaded Unique_ID.
I am puzzled by your "result" screenshot. I've not been able to create a Field picker list that includes the "Edit Advanced Favorites..." options shown at the bottom of the list in your screenshot. That's really weird. What version of Windows are you using?
I don't know what the limit is for the number of fields in a table. 1000 fields is a lot, but not all that big. The weirdness of seeing a list of commands in a drop down list that should be only fields looks like some sort of overrun error from very many fields in the list. I've reported that, just in case.
One last thing: a useful move for manual scrolling, is that if you start at the top of any of the dropdown Field lists, pressing the up arrow on the keyboard scrolls up through the list, rolling over to the bottom of the list. That's a quick way to manually pick any fields that appear at the very bottom of the list.