Playground: add minor Side-by-Side tool improvements #1819

Job	Run time
find_images_to_build	10s
build_image (modules/modeling/module_modeling_llm)	2m 20s
build_image (modules/programming/module_example)	2m 26s
build_image (modules/programming/module_programming_apted)	2m 8s
build_image (modules/programming/module_programming_llm)	2m 14s
build_image (modules/programming/module_programming_themisml)	4m 11s
build_image (modules/programming/module_programming_winnowing)	2m 9s
build_image (modules/text/module_text_cofee)	2m 32s
build_image (modules/text/module_text_llm)	2m 28s
build_image (assessment_module_manager)	2m 28s
build_image (llm_core)	2m 23s
build_image (log_viewer)	1m 49s
build_image (playground)	4m 1s
	31m 19s

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