Your phone won't be showing any kind of 'flashing was successful' or 'flashing wasn't successful' indicator depending if the flashing process was actually done, it will either boot up properly or it won't. There's a detailed log readout in Odin or Heimdall utility that states whether the flashing process did work or if there was some error. But just to repeat, if there is a hardware problem you cannot expect a software solution will be able to fix that. Or in other words, you can flash the firmware once or a dozen times, and that won't fix the problem.
A lock screen is pretty much a necessary practice, so no it's not 'bad news', but in this particular situation it adds a layer of complexity. Since you prefer not to reveal if your phone did or did not come with Lollipop, this is all just idle conjecture:
-- Encrypting the internal storage wasn't a default until Marshmallow. It was a big step forward for privacy concerns (trivia, Apple has always implemented full-disk hardware-based encryption for iPhones, a more resource-efficient, robust way than Android's after-the-fact, modular, firmware-based encryption scheme. But no worries, Android later stepped up its game to FBE, File Based Encryption, a more versatile implementation.)
-- The thing to keep in mind is while full-disk encryption was enabled by default when Marshmallow was released, it's something that had to be initially done at the factory, by the manufacturers. Encrypting the storage media needs to be done before the Android OS gets installed, and before the user starts using it and adding our own stuff. Encryption is a fundamental change that affects the file system itself, so if there's saved data it's wiped during the process. It's also a matter where if your phone was originally running Lollipop, if you later upgraded it to Marshmallow or Nougat, that did not necessarily change the internal storage from unencrypted to encrypted. It will remain in same state as before. So your S6 Edge may or may not have an encrypted internal storage media, it depends on if the phone came with Lollipop (it won't be) or Marshmallow (more likely it will be). The current version of Android (in your instance Nougat) isn't a factor as in order to actually do full-disk encryption would involve fully wiping the internal storage clean and installing the Android OS from scratch.
-- The issue regarding a lock screen is just incidental. In a normal situation, when you start up your phone it will go through a quick summation of the hardware, then the bootloader passes off the process so the Android OS gets loaded into memory. Part of that process involves the OS detecting and reading the encryption key(s) so data can be accessed and read off the internal storage. But in your current state, when there's a bootloop the OS can't be loaded into RAM, so the whole encryption matter isn't a factor anyway.
That $700 quote sounds reasonable. Data recovery from a phone that won't boot is a time-intensive process that involves a trained technician and an investment in the proper tools and equipment. It's not a matter of some high school kid plugging the phone into a magic box that reads off the data by pushing some buttons. The phone needs to be disassembled and the internal storage chip on the logic board has to be accessed.
For a better visualization, the iFixit site has some nice repair guides for your model. This one details your phone's internals (see step 11 that highlights the NAND storage chip):
https://www.ifixit.com/Teardown/Samsung+Galaxy+S6+Edge+Teardown/39158
There aren't a lot of viable options in this kind of situation. You can continue trying to find a magic fix for this, just be forewarned the Internet is saturated with lying trolls and there's no shortage of 'people' (a.k.a. 'bots') who claim such and such utility will fix anything for just a low price of whatever, so be judicious. I'd suggest you look forward and just get a new phone. Yeah, it's a pain in the a** to set up a new phone but at the same a new phone is going to be full of all kinds of new and different features and options.