The Berklee Introduction course says "Length, 6 weeks, effort, 5 hours per week". Do you really think 30 hours study is enough to "enter a PhD in music?" There's nothing wrong with paying for a certificate if having the certificate makes you feel good, and the course is probably fine (Berklee certainly has a good reputation) - but this is a very basic introduction to the subject, not the equivalent of a BA in music.
Comparing it with UK music exams like ABRSM, it doesn't look equivalent even to ABRSM Grade 5 which is about the same academic level as the UK school GCSE exams intended for 16-year olds, and you would take two more years of school courses, after that, and pass another exam, to qualify to start a BA music degree at university.
The Edinburgh course looks to be at a similar level - the web site clearly says "Level: Beginner". For example the first 3 weeks of the 5 are about "how to read basic music notation" - so more than half the course is the musical equivalent of "learning to read English in elementary school".
The Berklee "Music composition for Film, etc" is at a higher level, but read the first sentence of the Overview: "Gain the practical skills to compose, arrange, and orchestrate effective dramatic music for visual media, including film, television, and interactive media." This is a practical course, not an academic one to prepare you for an MA or PhD. Also, note that the admission requirements include submitting two original compositions in sheet music form, plus a video demo of your performing ability.
If you read the all the comments, you find this difference between the Berklee college courses and the online version:
While both degrees are from Berklee and share the same accreditation
from the New England Association of Schools and Colleges (NEASC), the
Bachelor’s of Music (BM) program has private lesson requirements,
ensemble/instrument lab requirements, audition requirements, and also
a different set of core music requirements. Otherwise, the BM and
Bachelor of Professional Studies (BPS) programs are the same. The
career opportunities for both programs are very similar. However, if
you are planning to later pursue graduate and/or doctoral studies,
some of these programs require that students have a BM from undergrad.