I think you have a misconception that Celtic language and culture covered much of Scotland up until fairly recently. However, large parts of Scotland haven’t spoken a Celtic language for the better part of a millennia, and the Scots Gaelic speaking people today have closer cultural and linguistic ties with the Irish than with medieval Scottish Celts. Since “Celtic culture” can be a bit tricky to define, I’ll stick to the linguistic history of Scotland and then look at Ireland for comparison.

The use of Celtic languages (which I’ll call Scots Gaelic) reached its peak in Scotland during the early 11th century. Even then, it was far from universal. Norse settlers from the Viking age spoke a Norse language in their settlements in the north and on the isles, and many of the border regions between the lowlands and Northumbria had not spoken a Celtic language since before the Anglo–Saxon invasion 500 years earlier. As Scottish and English royalty began to intermarry, the English-derived Scots language became the official language of the administration, and spread further up from the lowlands and into the north, pushing out both Gaelic and Norse speakers. This is all happening in the 12 and 11th centuries when Scotland was independent, and already Scots Gaelic was being pushed to the periphery centuries before the English attempted to subjugate Scotland, and ~500 years before English and Scottish union. Naturally, both of those events only increased the proliferation of the Scots and English languages over the Scots Gaelic. Of course the Scots Gaelic language suffered terribly in the aftermath of the Jacobite rebellions of the 18th century, and continues to decline to the present day – however it had been in decline long before that.

To answer your question though, Scotland does not promote the language as widely because most of the country has had no exposure to it in nearly 1000 years. The last Celtic language spoken in the Northumbrian border region wouldn’t even have been on the same branch of the Celtic language tree, let alone be mutually intelligible. Compare that to Ireland, where Irish was still the dominant language well into the 19th century. Its decline has much less to do with the natural proliferation of English, as was the case in Scotland. Rather, use of the English language was enforced much more strictly by the British. This was resented by early Irish nationalists, who tied the promotion of Irish language and culture very closely to their platforms. After Ireland gained its independence, this emphasis on the promotion of culture and language persisted, even as the language itself continues to struggle.