Compatibility with Mathematica 13.0+

[NicolasW1]

Neither loading nor using the package seems still to work in current versions of Mathematica.
Tested under Windows 10 with Mathematica 13.0, see the image below for the errors that appear.
Unfortunately, I was unable to pinpoint the problem any further by simply glancing over the code of the package.

[jkuczm]

Unfortunately I don't have access to version 13 to troubleshoot this.

From errors you show, it seems that builtin extension mapping is no longer stored in System`ConvertersDump`$extensionMappings.

Try loading package with following code:

Block[
  {
    System`ConvertersDump`$extensionMappings = {
      "*.3ds"->"3DS","*.aco"->"ACO","*.aif"->"AIFF","*.aiff"->"AIFF","*.au"->"AU","*.avi"->"AVI",
      "*.b64"->"BASE64","*.bdf"->"BDF","*.bmp"->"BMP","*.dib"->"BMP","*.rle"->"BMP","*.byu"->"BYU","*.bz2"->"BZIP2",
      "*.c"->"C","*.cdf"->"CDF","*.cif"->"CIF","*.col"->"DIMACS","*.col.b"->"DIMACS","*.csv"->"CSV","*.css"->"CSS","*.cur"->"CUR",
      "*.dae"->"DAE","*.dat"->"Table","*.dcm"->"DICOM","*.dic"->"DICOM","*.dicm"->"DICOM","*.dif"->"DIF","*.dot"->"DOT","*.dxf"->"DXF",
      "*.edf"->"EDF","*.emf"->"EMF","*.eml"->"EML","*.enc"->"UUE","*.ent"->"PDB","*.eps"->"EPS","*.epsf"->"EPS","*.epsi"->"EPS",
      "*.fcs"->"FCS","*.fsa"->"FASTA","*.fasta"->"FASTA","*.fa"->"FASTA","*.mpfa"->"FASTA","*.fq"->"FASTQ","*.fastq"->"FASTQ","*.fit"->"FITS","*.fits"->"FITS","*.flac"->"FLAC","*.flv"->"FLV",
      "*.g6"->"Graph6","*.gif"->"GIF","*.gml"->"Graphlet","*.grd"->"SurferGrid","*.grib"->"GRIB","*.grb"->"GRIB","*.gv"->"DOT","*.gw"->"LEDA","*.gxl"->"GXL","*.graphml"->"GraphML","*.gz"->"GZIP",
      "*.hdf"->"HDF","*.hmm"->"HMMER","*.htm"->"HTML","*.html"->"HTML","*.sds"->"HDF","*.h5"->"HDF5",
      "*.icc"->"ICC","*.icm"->"ICC","*.icns"->"ICNS","*.ico"->"ICO","*.ics"->"ICS",
      "*.jar"->"ZIP","*.jp2"->"JPEG2000","*.j2k"->"JPEG2000","*.jpc"->"JPEG2000","*.jpg"->"JPEG","*.jpeg"->"JPEG","*.jfif"->"JPEG","*.jvx"->"JVX",
      "*.kml"->"KML","*.kmz"->"KML",
      "*.lgr"->"LEDA","*.lmd"->"FCS","*.lwo"->"LWO",
      "*.m"->"Package","*.ma"->"Maya","*.mat"->"MAT","*.mbx"->"MBOX","*.mbox"->"MBOX","*.mesh"->"MESH","*.mgf"->"MGF","*.mid"->"MIDI","*.mml"->"MathML","*.mol"->"MOL","*.mol2"->"MOL2","*.mov"->"QuickTime","*.mp3"->"MP3","*.mtx"->"MTX","*.mulaw"->"AU","*.mx"->"MX",
      "*.nb"->"NB","*.nc"->"NETCDF","*.ndk"->"NDK","*.net"->"PAJEK","*.nex"->"NEXUS","*.noff"->"NOFF","*.nxs"->"NEXUS",
      "*.obj"->"OBJ","*.ods"->"ODS","*.off"->"OFF","*.oga"->"OGG","*.ogg"->"OGG",
      "*.pcx"->"PCX","*.pbm"->"PBM","*.pgm"->"PGM","*.ppm"->"PPM","*.pnm"->"PNM","*.png"->"PNG","*.pdb"->"PDB","*.pdf"->"PDF","*.pic"->"PXR","*.pic"->"PICT","*.pict"->"PICT","*.pct"->"PICT","*.ply"->"PLY","*.pov"->"POV","*.pxr"->"PXR",
      "*.qt"->"QuickTime",
      "*.raw"->"RawBitmap","*.rib"->"RIB","*.rtf"->"RTF",
      "*.sdf"->"SDF","*.sct"->"SCT","*.ch"->"SCT","*.ct"->"SCT","*.sff"->"SFF","*.sp3"->"SP3","*.stl"->"STL","*.s6"->"Sparse6","*.smi"->"SMILES","*.snd"->"SND","*.svg"->"SVG","*.svgz"->"SVGZ","*.swf"->"SWF",
      "*.tar"->"TAR","*.tex"->"TeX","*.tga"->"TGA","*.tgf"->"TGF","*.tgz"->"GZIP","*.tff"->"TIFF","*.tif"->"TIFF","*.tiff"->"TIFF","*.tsv"->"TSV","*.txt"->"Text",
      "*.uue"->"UUE",
      "*.w64"->"Wave64","*.wav"->"WAV","*.webp"->"WebP","*.wdx"->"WDX","*.wlnet"->"WLNet","*.wmf"->"WMF",
      "*.html"->"XHTML","*.htm"->"XHTML","*.xhtml"->"XHTML","*.xbm"->"XBM","*.xht"->"XHTML","*.xml"->"XML","*.xml"->"ExpressionML","*.xml"->"XHTML","*.xml"->"XHTMLMathML","*.xls"->"XLS","*.xlsx"->"XLSX","*.wrl"->"VRML","*.vtk"->"VTK","*.x3d"->"X3D","*.xyz"->"XYZ",
      "*.zip"->"ZIP","*.zpr"->"ZPR",
      "*.cha"->"HarwellBoeing","*.che"->"HarwellBoeing","*.cra"->"HarwellBoeing","*.cre"->"HarwellBoeing","*.csa"->"HarwellBoeing","*.cse"->"HarwellBoeing","*.cua"->"HarwellBoeing","*.cue"->"HarwellBoeing","*.cza"->"HarwellBoeing","*.cze"->"HarwellBoeing","*.pha"->"HarwellBoeing","*.phe"->"HarwellBoeing","*.pra"->"HarwellBoeing","*.pre"->"HarwellBoeing","*.psa"->"HarwellBoeing","*.pse"->"HarwellBoeing","*.pua"->"HarwellBoeing","*.pue"->"HarwellBoeing","*.pza"->"HarwellBoeing","*.pze"->"HarwellBoeing","*.rha"->"HarwellBoeing","*.rhe"->"HarwellBoeing","*.rra"->"HarwellBoeing","*.rre"->"HarwellBoeing","*.rsa"->"HarwellBoeing","*.rse"->"HarwellBoeing","*.rua"->"HarwellBoeing","*.rue"->"HarwellBoeing","*.rza"->"HarwellBoeing","*.rze"->"HarwellBoeing",
      "*.json"->"JSON",
      "*.bay"->"Raw","*.bmq"->"Raw","*.cr2"->"Raw","*.crw"->"Raw","*.cs1"->"Raw","*.dc2"->"Raw","*.dcr"->"Raw","*.dng"->"Raw","*.erf"->"Raw","*.fff"->"Raw","*.hdr"->"Raw","*.k25"->"Raw","*.kdc"->"Raw","*.mdc"->"Raw","*.mos"->"Raw","*.mrw"->"Raw","*.nef"->"Raw","*.orf"->"Raw","*.pef"->"Raw","*.pxn"->"Raw","*.raf"->"Raw","*.raw"->"Raw","*.rdc"->"Raw","*.sr2"->"Raw","*.srf"->"Raw","*.x3f"->"Raw","*.arw"->"Raw","*.3fr"->"Raw","*.cine"->"Raw","*.ia"->"Raw","*.kc2"->"Raw","*.mef"->"Raw","*.nrw"->"Raw","*.qtk"->"Raw","*.rw2"->"Raw","*.sti"->"Raw","*.rwl"->"Raw",
      "*.tex"->"TEX","*.latex"->"LATEX","*.tcx"->"TECHEXPLORER","*.tcx"->"TCX","*.css"->"CSS"
    }
  },
  Needs@"CellsToTeX`"
]

[NicolasW1]

This works and loads the package correctly (tested with Mathematica 13.0).