Structure of blocks matrix lost on broadcast or `similar`

using BlocksArrays, NamedArrays
m1 = mortar(NamedArray([rand(i,j) for i=1:2, j=1:3], (x=["a","b"], y=["c","d","e"])))
m2 = mortar(NamedArray([rand(i,j) for i=1:2, j=1:3], (x=["a","b"], y=["c","d","e"])))

m1 .* m2  # 2×3-blocked 3×6 BlockMatrix{Float64}

The result does not have the named blocks of the original matrices (although NamedArray itself preserves names on broadcast).
similar(m1) also has the blocks but not the names, which I guess might be the source of the problem?

Start by running the reproduction in the issue for m1 .* m2 and similar(m1), then trace the broadcast and similar entry points that construct the result. Compare their block structure and names with the original NamedArray inputs; done means both operations retain the named block structure described in the issue.