As Simon Brooks explains, Wales's divergence from the European norm can be traced from the mid-19th century onwards, when other European stateless nations, from Central and Eastern Europe to Ireland, were asserting themselves, and their distinct identities, to an extent to which Wales wasn't in our timeline (OTL.) They experienced cultural awakenings, demanded language rights, and developed their own autonomist and separatist political movements. Also, while the respective languages of these stateless nations were increasingly enhanced during this period, Welsh experienced the opposite; it was not championed in the same way, did not achieve the same language rights (such as being the medium of state primary or university education), and by 1914 became a minority language in Wales itself. But what if the Welsh in the long nineteenth century had followed the route that the Fins, Estonians and Czechs took, for example?
In this ATL, nineteenth century Wales, like Bohemia or Flanders, manages to industrialise without the Welsh language being eroded, and language campaigning manages to make Welsh the language of education in Wales just like it did other stateless languages in Central Europe. In addition, Wales like Ireland, sees the growth of its own Home Rule (ie political autonomy) movement from the 1870s onwards. In this ATL, the two general elections of 1910 still happen, and the House of Lords has its veto power removed, despite the fact that in this scenario, Lloyd George, rather than being the Liberal Chancellor of the Exchequer, is the leader of the Welsh nationalist party. These two elections, just like in our timeline, give the nationalists the balance of power, and Welsh and Irish Home Rule get passed into law in 1914. Now this is where Wales would be different from Ireland. There would be no Welsh Easter Rising since a key lead up to it was the creation of the two paramilitaries in Ireland during the Home Rule Crisis which was, of course, caused by Protestant Ulster's resistance to Home Rule. Wales does not have its own equivalent of Ulster which means that it is highly unlikely that a 'Welsh Volunteers' would be formed, and that guns would have been imported, like in Ireland. Without a Welsh Easter Rising, it is unlikely that Wales would have followed Ireland in rejecting moderate Home Rule-ism in favour of outright separatism. In other words, there would be no Welsh equivalent of Sinn Fein winning the election in 1918, and no Welsh war of independence. Wales would thus enter the 1920s with Home Rule, and not full independence.
However, let's for the sake of this scenario, say that Wales does elect a Welsh equivalent of Sinn Fein in 1918, and does proceed to fight a war of independence, and is granted Dominion status as the 'Welsh Free State' in 1922, before becoming a Republic after the Second World War, just as Ireland did.
But while I am sure that such a Wales would be doing very well now, the early years would have undoubtedly been difficult for the young nation. Ireland, after it gained its independence, had a civil war between those who accepted Ireland's Dominion status and partition, and those who settled for nothing short of a 32 county Ireland republic. Would ATL Wales also experience such tragedy? More certain though, is the fact that the Welsh Free State would have experienced significant economic hardship; Wales in the 1920s and 30s suffered particularly badly with its heavy industries being hit disproportionately hard by the downturn in international trade. There is no reason why an independent Wales could have changed this, and so in my opinion the first two decades would have still been a period of poverty and emigration, with a Welsh speaking diaspora in neighbouring England. Given the demographic of Wales and the success of the labour party in our OTL, it is highly likely that the Welsh Free State would have had a socialist government. Would this help Wales's situation? If not, would Wales's communist party and inter-war 'little Moscows' be more powerful in this independent Wales? Would a labour-ruled Wales be a 'one-party state', and if so, for how long? How would Wales's party political system develop?
Who ever would have been in power, they would have faced longer-term challenges as well; for example, how to make Wales more of a cohesive country that is better connected to itself. Even before the Beeching Cuts in the 1960s, it was remarked that Wales's north-south railway lines were not as good as the east-west routes - in short Wales's Victorian railway network was primarily designed to link north, mid and south Wales to England rather than to each other. If you are in north or Mid Wales, in OTL, one is often more likely to look to Chester, Liverpool, or Shrewsbury than to Cardiff. I would like to think that a Welsh government would chose to move the capital from Cardiff to Aberystwyth so as to make the country's population more evenly distributed, and give North and Mid-Wales a more natural economic and urban centre that is located within Wales itself.
However challenging its early years would have been, I imagine Wales today, like most small European countries, very wealthy and successful. In addition, this ATL Wales would not be on the 'edge' or 'periphery' of anything; Wales is located at the centre of the British Isles, between England and Ireland, and such an independent Wales would have been able to use it to its advantage in a way that it hasn't been able to as a peripheral part of the UK. But as an Englishman, I also feel that an independent and Welsh speaking Wales would have been good for us too. The five 'Anglo-Saxon' nations of the UK, New Zealand, Australia, the US and Canada are unusual compared to the other western nations in that only one of them, the US, shares a border with a non-English speaking country (one whom President Trump does not hold in high regard), and only in Canada does English share a country with another, non-minority, language. Every mainland European country, on the other hand, shares a land border with a foreign country that speaks a different language. This, I believe, has impacted us 'Anglo-Saxons', namely our outlook on the world, and has made us be more exceptionalist. Brexit, I believe, is an obvious result of this. I therefore believe that were England to share a border with an independent Welsh speaking Wales, it would have had a positive impact on us, and certainly changed our 'island mentality.