hl | text data using regular expressions ( efficient C program | Regex library

I´m trying to update existing contact using People service from Google apps gs. I have a contact like this:

I wanted a ArrayFormula at C1 which gives the required result as shown.

Entry sheet:
(Column C is my required column)

Date Entered is the date when the Name is Assigned a group i.e. a, b, c, d, e, f

Criteria:

1. The value of count is purely on basis of Date Entered (if john is assigned a on lowest date(10-Jun) then count value is 1, if rose is assigned a on 2nd lowest date(17-Jun) then count value is 2).
2. The value of count does not change even when the data is sorted in any manner because Date Entered column values is always permanent & does not change.
3. New entry date could be any date not necessarily highest date (If a new entry with name Rydu is assigned a on 9-Jun then the it's count value will become 1, then john's (10-Jun) will become 2 and so on)

Example:

After I sort the data in any random order say like this:

Random ordered sheet:
(Count value remains permanent)

And when I do New entries in between (Row 4th & 14th) and after last row (Row 17th):

Random Ordered sheet:
(Doesn't matter where I do)

1. ={"AF Formula1"; ArrayFormula(IF(B2:B="", "", COUNTIFS(B$2:B, "="&B2:B, D$2:D, <"&D2:D)+1))}
2. ={"AF Formula2";INDEX(IFERROR(1/(1/COUNTIFS(B2:B, B2:B, ROW(B2:B), "<="&ROW(B2:B)))))}

I tried to figure my own ArrayFormula but it's not working:

I got Formula for each cell:
=RANK($D2,FILTER($D$2:$D, $B$2:$B=$B2),1)
I figured out Filter doesn't work with ArrayFormula so I had to take a different approach.

I took help from my previous question answer (Arrayformula at H3) which was similar since in both cases each cell FILTER formula returns more than 1 value. (It was actually answered by player0)

Using the same technique I came up with this Formula which works absolutely fine :

=RANK($D2, ARRAYFORMULA(TRANSPOSE(SPLIT(VLOOKUP($B2, SUBSTITUTE(TRIM(SPLIT(FLATTEN(QUERY(QUERY({$B:$B&"×", $D:$D}, "SELECT MAX(Col2) WHERE Col2 IS NOT NULL GROUP BY Col2 PIVOT Col1", 1),, 9^9)), "×")), " ", ","), 2, 0), ","))), 1)

Now when I tried converting it to ArrayFormula: ($D2 to $D2:$D & $B2 to $B2:$B)

=ARRAYFORMULA(RANK($D2:$D,TRANSPOSE(SPLIT(VLOOKUP($B2:$B, SUBSTITUTE(TRIM(SPLIT(FLATTEN(QUERY(QUERY({$B:$B&"×", $D:$D}, "SELECT MAX(Col2) WHERE Col2 IS NOT NULL GROUP BY Col2 PIVOT Col1", 1),, 9^9)), "×")), " ", ","), 2, 0), ",")), 1))

It gives me an error "Did not find value '' in VLOOKUP evaluation", I figured out that the problem is only in VLOOKUP when I change $B2 to $B2:$B.

I'm sure VLOOKUP works with ArrayFormula, I fail to understand where my formula is going wrong! Please help me correct my ArrayFormula.

Here is the editable sheet link

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