Irish Genealogy Toolkit is a guide to Irish family history.
https://www.irish-genealogy-toolkit.comChurch records section is under Genealogy tab. There is a link to "List of Church of Ireland Parish Registers".
Another section under "Genealogy" tab is "Land Records". Reading this and following up the links might help to explain your enquiry about valuation records in another topic.
Irish Genealogy.ie is the website for births, marriages and deaths (BMDs from 1864, non-R.C. marriages from 1845). It also has transcriptions of church records for a few dioceses and counties.
https://www.irishgenealogy.ie/en/There is an overseas births register (GRO in England) which includes some regimental births from late 18th century. It's likely that if babies of soldiers born in Ireland were baptised there they would be in registers of local churches, unless there was a chapel at the barracks or a regimental chaplain. Only a small number of soldiers' wives were officially allowed to accompany their husbands. Others went unofficially and lived outside the barracks.
People from Wales, England and Scotland had been living in Ireland for hundreds of years before your ancestor was born.
Norman invasion of Ireland 1269-1271. Invasion force was made up of Norman, Flemish and Welsh. Leader of the invasion, the Norman lord, Richard de Clare, was Earl of Pembroke in Wales. Some Welsh settlers followed.
A common surname in Ireland is Walsh (Walsh or Welsh, a foreigner or a Briton).
"The Norman Invasion of Ireland" by Richard Roche. (Roche surname has Welsh origins.)
Later Welsh movement to Ireland.
"From Soldier to Settler: the Welsh in Ireland 1558-1641", a thesis by Rhys David Morgan (2011)
https://orca.cardiff.ac.uk/54180/