High quality movies and multi-tab browsing will not benefit much from a dedicated GPU as the iGPU will be more than ample to play them back.
Photoshop can benefit from a GPU depending on your workload, but it's usually a very specific workload. Tech Notice tested Photoshop 25 with PugetBench 0.93.7 and found only about an 11% performance improvement from the lowest performing RTX 4060 to the top performing Intel ARC A770. My own personal usage I've found that having 64GB of RAM is more important than having a ultra high performance GPU for Photoshop in my work load.
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Adobe Lightroom benefits even less from GPUs except while exporting large amounts of photos and possibly with upcoming AI features.
Any of the coolers you mentioned will cool a 5600G CPU. In terms of how quiet they are, you may want to try using different fans than stock.
450W is more than enough for an APU build. It will be adequate for GPUs below 200 watts. Choose a power supply that shuts off the fan when under low loads to improve the acoustic performance.
Generally, I recommend that you get a more featured mainboard when the budget allows as you it's easier to upgrade in the future. I have a Gigabyte B550 ITX board in my most recent build. Other than the wi-fi module failing (which I personally don't need), it's been good.
