Although I’m unsure on how to achieve this in php, within javascript you can change the category by hooking into the blocks.registerBlockType
hook.
Here is a small example how it would work, although I’d recommend using lodash to deepClone the settings object to keep everything immutable.
const rearrangeBlockCategories = {
'core/table': 'common',
};
wp.hooks.addFilter('blocks.registerBlockType', '[namespace]', (settings, name) => {
if (rearrangeBlockCategories[name]) {
settings.category = rearrangeBlockCategories[name];
}
return settings;
});