Currently the best-scoring solution that fits in an answer!

The total byte count is "only" 6694 3394 3354, and so you can try it online!

Additionally, if an operator is the first input to a function, it gets turned into a string so that the function can use it. This means that we can avoid the quotes if we just make every run of parentheses 1 byte shorter, and split on > instead (with some clever arrangement to cancel out the resulting >) in the code):

Currently the best-scoring solution that fits in an answer!

The total byte count is "only" 6694 3394 3354, so you can try it online!

Additionally, if an operator is the first input to a function, it gets turned into a string so that the function can decide what to do with it. This means that we can avoid the quotes if we just make every run of parentheses 1 byte shorter, and split on > instead (with some clever arrangement to cancel out the resulting >) in the code):

Japt, 19 14 13 10 9 bytes

"()()...()()<"q> m(l)m(d)q

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The total byte count is "only" 6694 3394 3351, and so you can try it online!

q">" mZ{Zl d} q""

which is a quite literal description: .split("<>").map(Z => Z.length.toChar()).join("") Now we need to minimize non-bracket chars. How? Well, first we can do some actual golfing:

q"<>" ml md q

This roughly represents .split("<>").map(Z => Z.length).map(Z => Z.toChar()).join().

q("<>")m(l)m(d)q

Additionally, if an operator is the first input to a function, it gets turned into a string so that the function can use it. This means that we can avoid the quotes if we just make every run of parentheses 1 byte shorter, and split on > instead:

"...<"q> m(l)m(d)q

This saves us a further byte, since we took out the quotes and added a space.

Japt, 19 14 13 10 9 8 bytes

"(()()...()()<"q>)m(l)m(d)q

(()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()())<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()())<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()<>()()()()()()()()()()()()()()()()<>()()()()()()<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()())<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()<>()()()()()()()()()()()()()()())<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()())<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()())<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()<>()()()()()()()()()()()()()()()()()()()()())<>()()()()()()()()()()()()()()()(<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()())<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()())<>()()()()()()()()()()()()()()()()()()()()()()<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()(<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()())<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()<>()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()<>()()()()()()()()()()()()()()()()<

The total byte count is "only" 6694 3394 3354, and so you can try it online!

"..."q"<>" mZ{Zl d} q""

which is a quite literal description: "...".split("<>").map(Z => Z.length.toChar()).join("") Now we need to minimize non-bracket chars. How? Well, first we can do some actual golfing:

"..."q"<>" ml md q

This roughly represents "...".split("<>").map(Z => Z.length).map(Z => Z.toChar()).join().

"..."q("<>")m(l)m(d)q

Additionally, if an operator is the first input to a function, it gets turned into a string so that the function can use it. This means that we can avoid the quotes if we just make every run of parentheses 1 byte shorter, and split on > instead (with some clever arrangement to cancel out the resulting >) in the code):

"(...<"q>)m(l)m(d)q

This saves us a further two bytes, since we took out two of the quotation marks.