You can get in early somewhere with "just" a BSc in Alchemy, you've definitely chose the best route, congrats.
I'd say that both MSc and lab-work would help, either/or or both..... but actual work in a lab will always help much more than just a qualification
anyway, randomly drifting away, wildly from your sensible questions, and hoping to attract more attention; I have (Chemist) friends who have left the UK, for forensic or similar science based jobs - bit of a shock, but it's easy to triple your 'expected' local salary
Whilst Scotland actually has a Forensic Science service, rest of UK (probably) has something akin to "the cheapest bidder' who have even allegedly made-stuff-up.
https://www.spa.police.uk/work-with-us/how-to-apply/ (register there & see how it goes), maybe their application form only has space for postgrad quals? I always apply to these 'generic applications' as CERN actually kept me on their 'maybe' list for 2 years, then phoned me up when they had a suitable job. I did it later with my curent research centre job, I applied, then almost forgot about it, again for a year or so.
Forensics AUS seems to have state by state services, you'd have to do more searches there
whilst NZ have a bit of career guidance here
https://www.careers.govt.nz/jobs-database/science/science/forensic-scientist/also, a bit away from truly competitive forensics, in a fortnight I think we'll probably still be a member of EMBL, they do sponsor MSc, sometimes from a chem background. in fact from any STEM background (UK's EMBL is Hinxton, Cambridgeshire)
https://www.embl.org/jobs/#group=data-group-1Jobs in "light" general
https://elmi.embl.org/category/jobs/contacts in "imaging"
https://elmi.embl.org/home/elmi-members/elmi-members-in-the-united-kingdom/some fellowships related to EMBL,
https://www.embl.org/training/technology-developers-programme/arise/Total of 350 internships here?
https://www.embl.de/training/undergraduates/index.html