filter a table based on a list [UPDATED]

I have a table of data.  Each row/record has a unique identifier.

I have a separate list of unique identifiers that is a subset of those in the full table.

I want to see the data for only the records on my list.

All the data, i.e. every column, regardless of how many columns there are.

Here's an oversimplified example:

I have this table of data:

I have this list:

Desired end result is:

Except I need a couple hundred records out of a few thousand.    Essentially, out of these zillions of records, show me only the ones on this list.

Current approach is manual brute force; add the target list as new rows to the original table, apply conditional formatting to that column to highlight those identifiers that are now duplicated, filtering that column on that format, and then filtering on a data column to exclude blank cells.  Not particularly elegant.

Other hackey solutions we've come up with:

• manually choosing the records I want from the drop-down filter menu on the column header - not practical with a lot of records.
• creating a helper column to filter has the same problem with high volumes - each record has to be located and interacted with directly.
• Doing a vlookup to specify each column individually; inefficient with lots of columns, plus it can't adapt to a change in the number of columns in the table.

What obvious answer am I overlooking?

[Updated to add example / for clarity]