I am Arch GNU/Linux user who usually manages almost every package with pacman; I manage TeX and LaTeX-related things with tlmgr. I installed tlmgr from source.

I am writing paper. I would like to use bibliography.

When I tried latexmk -pdflua main.ltx:

Rc files read:
  latexmkrc
Latexmk: This is Latexmk, John Collins, 20 November 2021, version: 4.76.
Latexmk: applying rule 'biber main'...
Rule 'biber main': The following rules & subrules became out-of-date:
      'biber main'
------------
Run number 1 of rule 'biber main'
------------
------------
Running 'biber  "main.bcf"'
------------
biber: error while loading shared libraries: libcrypt.so.1: cannot open shared object file: No such file or directory
Latexmk: Errors, so I did not complete making targets
Collected error summary (may duplicate other messages):
  biber main: Could not open biber log file for 'main'
Latexmk: Use the -f option to force complete processing,
 unless error was exceeding maximum runs, or warnings treated as errors.

libcrypt.so* on my environment

$ pacman -Qo /usr/lib/libcrypt*
/usr/lib/libcrypto.so is owned by openssl 1.1.1.m-1
/usr/lib/libcrypto.so.1.1 is owned by openssl 1.1.1.m-1
/usr/lib/libcryptsetup.so is owned by cryptsetup 2.4.3-2
/usr/lib/libcryptsetup.so.12 is owned by cryptsetup 2.4.3-2
/usr/lib/libcryptsetup.so.12.7.0 is owned by cryptsetup 2.4.3-2
/usr/lib/libcrypt.so is owned by libxcrypt 4.4.28-1
/usr/lib/libcrypt.so.2 is owned by libxcrypt 4.4.28-1
/usr/lib/libcrypt.so.2.0.0 is owned by libxcrypt 4.4.28-1

What I tried else

I uninstalled and re-installed biber on tlmgr but did not work.

# ln -s /usr/lib/libcrypt.so /usr/lib/libcrypt.so.1
$ latexmkrc -pdflua main.ltx
Rc files read:
  latexmkrc
Latexmk: This is Latexmk, John Collins, 20 November 2021, version: 4.76.
Latexmk: applying rule 'biber main'...
Rule 'biber main': The following rules & subrules became out-of-date:
      'biber main'
------------
Run number 1 of rule 'biber main'
------------
------------
Running 'biber  "main.bcf"'
------------
/tmp/par-716861/cache-0e6aa298f0c2e7a775de99938825b2d56bd2027f/biber: /usr/lib/libcrypt.so.1: version `GLIBC_2.2.5' not found (required by /tmp/par-716861/cache-0e6aa298f0c2e7a775de99938825b2d56bd2027f/biber)
Latexmk: Errors, so I did not complete making targets
Collected error summary (may duplicate other messages):
  biber main: Could not open biber log file for 'main'
Latexmk: Use the -f option to force complete processing,
 unless error was exceeding maximum runs, or warnings treated as errors.

File source

latexmkrc:

$latex='lualatex %O -synctex=1 -interaction=nonstopmode %S';
#$bibtex='upbibtex %O %B';
$bibtex='biber %O %B';
$makeindex='upmendex %O -o %D %S';
$pdf_mode=3;