Convert GeoPackage (GPKG) to EPSG:27700 (British National Grid)

I have a GeoPackage (.gpkg) file containing spatial data (attached), but I need it reprojected to EPSG:27700 (British National Grid). I keep getting the following error when using the file. Unfortunately, I lack the technical expertise to do this myself and need an experienced GIS professional to assist.

Requirements:

Convert the GeoPackage (.gpkg) file to EPSG:27700.
Handle any issues related to MultiPolygons or invalid geometries.
Ensure that all attributes and geometries remain intact after transformation.
Deliver a correctly formatted GeoPackage (.gpkg) file with the new projection.
Ideal Candidate:

Expertise in QGIS, ArcGIS, GDAL, or GeoPandas.
Experience working with GeoPackage files and coordinate transformations.
Ability to troubleshoot and resolve geometry errors (e.g., invalid geometries or MultiPolygon handling).
Deliverables:

A correctly reprojected GeoPackage (.gpkg) file in EPSG:27700 format.
A brief summary of any fixes applied to ensure valid geometries.