Install the pug tmbundle, then edit the built-in HTML bundle to append this above the style pattern

textmate 2 pug html embed.txt

				{	begin = '(^[ \t]+)?(?=<(?i:template lang="pug")(?!-))';
					end = '(?!\G)([ \t]*$\n?)?';
					beginCaptures = { 1 = { name = 'punctuation.whitespace.embedded.leading.html'; }; };
					endCaptures = { 1 = { name = 'punctuation.whitespace.embedded.trailing.html'; }; };
					patterns = (
						{	name = 'meta.embedded.block.html';
							begin = '(?i)(<)(template)(?=\s|/?>)';
							end = '(?i)((<)/)(template)\s*(>)';
							beginCaptures = {
								0 = { name = 'meta.tag.metadata.pug.start.html'; };
								1 = { name = 'punctuation.definition.tag.begin.html'; };
								2 = { name = 'entity.name.tag.html'; };
							};
							endCaptures = {
								0 = { name = 'meta.tag.metadata.pug.end.html'; };
								1 = { name = 'punctuation.definition.tag.begin.html'; };
								2 = { name = 'source.pug'; };
								3 = { name = 'entity.name.tag.html'; };
								4 = { name = 'punctuation.definition.tag.end.html'; };
							};
							patterns = (
								{	name = 'meta.tag.metadata.pug.start.html';
									begin = '\G';
									end = '(>)';
									captures = { 1 = { name = 'punctuation.definition.tag.end.html'; }; };
									patterns = ( { include = '#attribute'; } );
								},
								{	name = 'source.pug';
									begin = '(?!\G)';
									end = '(?=</(?i:template))';
									patterns = ( { include = 'source.pug'; } );
								}
							);
						},
					);
				},