Building a context-free grammar for this language
I'm not sure to have fully understood your notation.

As production rules you could consider:

$S \rightarrow aSa \ |aSb \ | S_1 | \epsilon$

$S_1 \rightarrow bS_1a | \ bS_1b \ | \ \epsilon$

In $S$ for each $a$ you add an $a$ or a $b$ or you can go to $S_1$ and then never come back to $S$ again.

In $S_1$ for each $b$ you add an $a$ or a $b$.