Here is a snip.
Does anyone know the recommended image size for the quick links so it looks good?
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The OOTB picture size for Client Side Quick Link Web Part is
379px x 213px while the rendering canvas/surface size is
377px x 209px. See below:
Note: since the modern web part use Office Fabric for UI, which is responsive in nature, the above mentioned resolutions are majored on a full HD monitor. It may vary based on screen size. But I, guess if you maintain the aspect ratio, you image will display in proper manner.