How to paste a pattern based on a FILENAME using awk

Question

Template A.tsv:

Name    data
B
C

And several files to analyse, for example, B.txt:

#bla
#blabla
16  LSD

and C.txt:

#bla
#blabla
16  ARH

I want to add OK or KO to A.tsv based on whether LSD is present in the other files:

Name    data
B   OK
C   KO

The field separators are tabs (\t) for all files. How to do that with awk?

I started with FILENAME recognition but no clue for the rest:

template="A.tsv"
for bla in data/*.txt ; do
r="$(basename -s ".txt" $bla)"
( head -n 1 $template
awk -F'\t' -v OFS="\t" -v filename=$r  [..........] >> output_final.tsv;
done

Answer 1

awk '
  !last && /LSD/{seen[FILENAME]=1; nextfile;}
  last{
    if (FNR<2) print
    else print $1 "\t" ( seen[$1".txt"] ? "OK" : "KO" )
  }
' *.txt last=1 A.tsv

First Awk reads the txt files, for which last is unset, and looks for a LSD match. If found, it puts the filename in the seen array (nextfile is just an optimization). When it reaches the A.tsv file last is set, so it prints its header and checks for each remaining line if the corresponding filename is in seen, adding <tab>OK if yes and <tab>KO if not.