The hardware information:
What Linux Operating System would be suitable for running BYOND DreamMaker?

Hardware Overview:

Model Name: MacBook
Model Identifier: MacBook10,1
Processor Name: Dual-Core Intel Core m3
Processor Speed: 1.2 GHz
Number of Processors: 1
Total Number of Cores: 2
L2 Cache (per Core): 256 KB
L3 Cache: 4 MB
Hyper-Threading Technology: Enabled
Memory: 8 GB
Boot ROM Version:
SMC Version (system): 2.42f12
Serial Number (system): C02V23BJHH21
Hardware UUID: 6D1BCC59-5B42-5134-BC2E-99298C8A0D43
I don't think you'll get decent performance out of any virtualization with a processor like that on Linux. Your best bet is probably Windows XP or Windows 7.

If you have a dedicated GPU, you may be able to get qemu and kvm working alright. If you don't, forget about it.

You can install Wine on any linux distribution. A lightweight ubuntu would be decent (Linux Mint, Lubuntu, Xubuntu, Ubuntu MATE) and easy to use.

Manjaro runs it very well (it is what I use), also good for beginners but it is a rolling release system so it has its fair share of issues and I think the system requirements may ask for a morr powerful processor.

Bohdi Linux is another good option, but personally I would stick to the ubuntu or arch ecosystem. They are both highly evolved and beginner-friendly.

No thank you!

Not bootlegging Windows operating system, O please(!) for HAL's international business machine tabulating all over my XacmaByond environment. Thus, not going to Wine. Those happen during performance blogging partnership evenings on Wednesdays. #rrr247

Enough with acronyms, thank you. Graphics processing unit on this device:
Intel HD Graphics 615:

Chipset Model: Intel HD Graphics 615
Type: GPU
Bus: Built-In
VRAM (Dynamic, Max): 1536 MB
Vendor: Intel
Device ID: 0x591e
Revision ID: 0x0002
Metal: Supported, feature set macOS GPUFamily2 v1

Parallels wishes me to choose what Linux flavour: Ubuntu Linux, Fedora Linux, CentOS Linux, Debian GNU/Linux, Mint Linux.

Android, MacOS and Microsoft Edge and IE Test Environments are also other options.

I don't need ubuntu since my Google PixelBook pleases me no end (Google chose ubuntu as their platform) but the experiment to run BYOND on the PixelBook ended up with me downloading and using Wine.

Emulation of running a 'Windows' virtual machine did not please me as the screen size of 'DreamMaker' can not fit my PixelBook screen.

At the moment, an external hard drive has been connected to my MacBook Pro and the drive is waiting for Parallels to either read the ubuntu flavour on this external hard drive disc || I shall connect the solid state disc and let Parallels read that next.

"arch ecosystem"
Just to clear this up: Wine is not a bootleg Windows environment.

But at least we know your GPU certainly isn't going to help the situation then. I don't think your computer will run really any modern OS well in Parallels without a dedicated GPU.

I don't know what kind of support you're looking for. DreamMaker is command-line only on Linux (arguably useless if you cannot test anything or design maps, interfaces, etc...). You will need to run Wine.

Since you have another hard drive, perhaps dual booting is not out of the question?

That computer would struggle to run modern BYOND games using Windows native, honestly.
CrossOver seems to work better with Catalina operating system than WINE.