Learn English – single word for “But anyway”

Yet is a somewhat rare alternative to but, yet it is well suited to the usage in question:

yet – adverb 3 – Nevertheless; in spite of that:

‘every week she gets worse, and yet it could go on for years’

– OxfordDictionaries.com

And may be omitted before yet, as in the first sentence of this answer, leaving an equally acceptable variation of the dictionary example:

‘every week she gets worse, yet it could go on for years’