Switching the coordinate system dynamically in Leaflet

Question

I am trying to change the coordinate system in Leaflet using proj4 and proj4leaflet.

If I execute this code

proj4.defs("EPSG:20538","+proj=utm +zone=38 +ellps=krass +towgs84=-43,-163,45,0,0,0,0 +units=m +no_defs +type=crs");

var crs = new L.Proj.CRS('EPSG:20538',
proj4.defs('EPSG:20538'),
{
    origin: [0, 0],
    resolutions: [
        4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, 0.5
    ],
    bounds: L.bounds([52393.99, -190270.05], [1221571.98, 1338148.68])
});

let map = L.map('map', {
    zoom: 6,
    crs: crs,
    minZoom: 2,
    maxZoom: 20,
    maxBoundsViscosity: 1.0,
    // worldCopyJump: true,
    attributionControl:false,
    zoomControl: false,
    almostSamplingPeriod: 10,
    almostDistance: 25
});

then everything works, the coordinate system is changed.

You can see it in the screenshots below. Image from https://epsg.io/ and my map

But if I try to load data from JSON file on the server like this

let map = L.map('map', {
    zoom: 6,
    minZoom: 2,
    maxZoom: 20,
    maxBoundsViscosity: 1.0,
    // worldCopyJump: true,
    attributionControl:false,
    zoomControl: false,
    almostSamplingPeriod: 10,
    almostDistance: 25
});

async function applyCrsToMap(data) {
    if (data.name === "EPSG:3857") {
        map.options.crs = L.CRS.EPSG3857;
    } else {
        proj4.defs(data.name, data.proj4);
        
        let newCrs = new L.Proj.CRS(data.name, proj4.defs(data.name), {
            origin: [0, 0],
            resolutions: [
                2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, 0.5
            ],
            bounds: L.bounds(data.bounds[0], data.bounds[1])
        });

        map.options.crs = newCrs;
    }

I get the wrong image on the map. A rectangle of solid color in the middle of an empty map.

It disappears if I zoom out of the map. Nothing works and the map is gone. My wms server is working and configured correctly, it outputs the correct tiles as in the first case. In the second case I am just loading data from a json file and I don't understand why it doesn't work. The data comes in JSON format for proj:

"EPSG:2001": {
      "name": "EPSG:2001",
      "proj4": "+proj=tmerc +lat_0=0 +lon_0=-62 +k=0.9995 +x_0=400000 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-255,-15,71,0,0,0,0 +units=m +no_defs +type=crs",
      "center": [423637.34, 1888160.65],
      "bounds": [[405547.46, 1872662.17], [441754.25, 1903675.41]]
    }

I have a WMS server: L.tileLayer.wms.

function setWMSLayer(theme) {
    if (!theme.includes("SeaChart_")) theme = "SeaChart_" + theme;
    const url = `http://${FLASK_HOST}/cgi-bin/mapserv?map=/var/www/s57demo/data/map/${theme}.map`;
    wmsLocal.setUrl(url);
    wmsLocal.setParams({
        layers: theme
    });
}

const wmsLocal = L.tileLayer.wms('', {
    noWrap: false
});

It uploads .map files with the configuration of my map layers. Each .map file looks something like this:

MAP
    NAME SeaChart_DAY_BLACKBACK
    SIZE 1000 1000
    UNITS dd
    EXTENT -180 -90 180 90
    MAXSIZE 32768
    # CONFIG "MS_OPENLAYERS_JS_URL" "http://localhost/LocalOpenLayers/OpenLayers-ms60.js"
    CONFIG "MS_ERRORFILE" "/tmp/SeaChart_DAY_BLACKBACK.log"
    DEBUG 5
    CONFIG "ON_MISSING_DATA" "LOG"
    #RESOLUTION 96
    #DEFRESOLUTION 96

    PROJECTION
         'init=epsg:4326'
    END

    IMAGETYPE png
    FONTSET './fonts/fontset.lst'
    SYMBOLSET "./symbols/symbols-day.map"
    OUTPUTFORMAT
        NAME 'AGG'
        DRIVER AGG/PNG
        IMAGEMODE RGB
    END

    SHAPEPATH "../chart"

    WEB
        IMAGEPATH '/tmp/'
        IMAGEURL '/tmp/'

        METADATA
          "ows_enable_request"   "*"
          'ows_title'           'SeaChart_DAY_BLACKBACK'
          # 'ows_onlineresource'  'http://localhost/cgi-bin/mapserv.fcgi?map=/app/output/map/SeaChart_DAY_BLACKBACK.map&'
          "wms_srs" "EPSG:4326 EPSG:3857 EPSG:2950 EPSG:2949 EPSG:32188 EPSG:32187 EPSG:42403 EPSG:3857 EPSG:3979"
          "wfs_srs" "EPSG:4326 EPSG:3857 EPSG:2950 EPSG:2949 EPSG:32188 EPSG:32187 EPSG:42403 EPSG:3857 EPSG:3979"
          "labelcache_map_edge_buffer" "10"
          "wms_bbox_extended" "true"
        END
    END

    #
    #   Dummy layer to create a layer group for the color mode
    #
    LAYER
        NAME "DAY_BLACKBACK"
        GROUP "default"
        TYPE POINT
        TRANSFORM FALSE
        STATUS ON
        FEATURE
            POINTS 1 1 END
        END
    END

    #INCLUDE_GSHHS_HERE

END # Map

I use MapServer to load map tiles at this path - http://${FLASK_HOST}/cgi-bin/mapserv?map=/var/www/s57demo/data/map/${theme}.map.

I think the problem in Leaflet but I don't understand what exactly the problem is.