What's the best weight training app that works with Watch 5 pro and at the end of the session that synchronises with Samsung health app
I do not think that you will find a training app that will share data with Samsung Health App. There is the Health Platform that collects data from the different supported devices.
I do not know of any device in particular that might be useful to you, but my advise is to look at the list of devices that are supported by Samsung Health App. Of course this has the disadvantage of purchasing another device, which might not be what you are looking for.
Anyway, if you wish to check the compatible devices, Open the Samsung Health App, tap on the three vertical dots to open settings, Tap on Settings and then on Accessories. There is a list of supported accessories by category. I do not know if any of those will be good to you for weight training, but it is worth a try. Please check the webpage of the device for full specifications before getting one, just to check that it might be right for you.