Blender addon to convert a curve to a mesh while preserving modifiers. Tested on Blender 3.5.

curve_to_mesh_preserving_modifiers.py

from typing import Any, NamedTuple

import bpy


class ModifierSpec(NamedTuple):
    name: str
    type: str
    properties: dict[str, Any]

    @classmethod
    def from_modifier(cls, modifier):
        spec = cls(modifier.name, modifier.type, {})

        for prop in modifier.bl_rna.properties:
            if prop.is_readonly:
                continue

            name = prop.identifier
            spec.properties[name] = getattr(modifier, name)

        return spec

    def add_to_object(self, obj):
        new_modifier = obj.modifiers.get(self.name, None)
        if new_modifier is None:
            new_modifier = obj.modifiers.new(self.name, self.type)

        for name, prop in self.properties.items():
            setattr(new_modifier, name, prop)


class ConvertCurvePreservingModifiersOperator(bpy.types.Operator):
    bl_idname = "object.convert_curve_preserving_modifiers"
    bl_label = "Convert Curve to Mesh Preserving Modifiers"
    bl_description = "Converts a NURBS path to mesh while preserving modifiers"

    @classmethod
    def poll(cls, context):
        return len(context.selected_objects) > 0 and any(
            obj.type == "CURVE" for obj in context.selected_objects
        )

    def execute(self, context):
        initial_active_object = bpy.context.view_layer.objects.active

        for obj in list(context.selected_objects):
            if obj.type != "CURVE":
                continue

            # collect modifiers from object
            modifier_specs: list[ModifierSpec] = []
            for old_modifier in obj.modifiers:
                modifier_specs.append(ModifierSpec.from_modifier(old_modifier))

            # make the object the active one
            bpy.context.view_layer.objects.active = obj

            # convert to mesh
            bpy.ops.object.convert(target="MESH")

            # add modifiers from spec
            for spec in modifier_specs:
                spec.add_to_object(obj)

        # select the previously-selected objects again
        bpy.context.view_layer.objects.active = initial_active_object

        return {"FINISHED"}


class ConvertCurvePreservingModifiersPanel(bpy.types.Panel):
    # arbitrary id thing
    bl_idname = "OBJECT_PT_convert_curve_preserving_modifiers"
    # show in UI
    bl_region_type = "UI"
    # only show in the viewport editor
    bl_space_type = "VIEW_3D"
    # show in the "Tool" tab
    bl_category = "Tool"
    # name of the panel header
    bl_label = "Convert Curve Preserving Modifiers"

    def draw(self, context):
        layout = self.layout

        row = layout.row()
        row.operator(
            "object.convert_curve_preserving_modifiers",
            text="Convert selected curves",
        )


# Register the operator and panel
classes = (
    ConvertCurvePreservingModifiersOperator,
    ConvertCurvePreservingModifiersPanel,
)

bl_info = {
    "name": "Convert Curve to Mesh Preserving Modifiers",
    "blender": (3, 2, 0),
    "category": "Object",
}


def register():
    for cls in classes:
        bpy.utils.register_class(cls)


def unregister():
    for cls in classes:
        bpy.utils.unregister_class(cls)