A word is (i) a °free °morph, or (ii) a °clitic, or (iii) a °root or a °compound possibly augmented by nonrequired affixes and augmented by required affixes if there are any.
The definition given here is from Haspelmath (2023). It does not define "word" as a "natural" concept, but it is largely in line with the way linguists use the term. The definition indicates that "word" can hardly be a basic concept of grammar, and if the morphology/syntax division is based on the "word" concept, it can hardly be a basic architectural division.
The notion of "required affix" (= an affix that must be present in a free form unless it is replaced by another affix) has not played a role in the earlier literature, but it seems to be needed to exclude stems such as Latin lup- 'wolf'. This stem is a root but not a word, because a case-number affix is required (e.g. lup-us 'wolf.NOM.SG', lup-orum 'wolf.GEN.PL').
"The notion of ‘word’ covers a number of interrelated concepts. A ‘phonological word’ as a minimally pronounceable unit is recognized on phonological criteria. A ‘grammatical word’ is recognized on exclusively grammatical – morphological and syntactic – principles." (Aikhenvald et al. 2020: 1)