fix(producer): scope per-instance variables for repeated sub-composition mounts #10957

Job	Run time
Detect changes	14s
Preflight (lint + format)	43s
regression-shards (shard-2, style-15-prod hdr-hlg-regression style-1-prod many-cuts vfr-screen-re...	22m 21s
regression-shards (shard-7, sub-composition-video style-18-prod raf-ball-render-compat font-varia...	21m 7s
regression-shards (shard-8, style-13-prod style-6-prod vignelli-stacking gsap-letters-render-comp...	23m 14s
regression-shards (shard-4, style-16-prod style-9-prod style-17-prod iframe-render-compat variabl...	23m 23s
regression-shards (shard-6, overlay-montage-prod style-12-prod chat missing-host-comp-id png-sequ...	19m 7s
regression-shards (shard-1, hdr-regression style-5-prod style-3-prod mov-prores)	19m 59s
regression-shards (shard-5, style-4-prod style-11-prod style-2-prod animejs-adapter typegpu-adapt...	23m 24s
regression-shards (shard-3, style-7-prod style-8-prod style-10-prod css-spinner-render-compat web...	20m 28s
regression	3s
	2h 54m 3s

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