The 1906-22 Liberal-led governments gave the UK progressive taxation, unemployment benefits, the state pension, the first tax-funded healthcare, the end of the primacy of the House of Lords. This was one of the most transformational progressive governments in our country's history and this is partly why they were winning by-elections in working-class seats right up to the start of the First World War.
I think you're overestimating the existence of underlying 'political' causes of the rise of Labour and underestimating the pure 'electoral' factors around the Asquith/Lloyd George split.
You can't just say 'austerity' every time a Chancellor decides not to spend even more money...
Government spending in the UK today accounts for 45% of GDP. The state that the Tories have bequeathed to Labour represents a significantly larger share of the UK economy than it did at any point in Gordon Brown's decade as Chancellor. The state today is bigger than it was when the Atlee government left office. In fact the only post-WW2 years in which the state has been bigger than in the Sunak years were very briefly for a couple of years in the mid-1970s and then in 2009-11. The only people in this country for whom a state of today's size is normal relative to most of their life experiences are toddlers who were born in the Johnson/Truss/Sunak era.
By all means argue for a more massive state if you like. But we're not living in austere times.