Open back headphones will be significantly better than closed but you’ll also need a competent headphone DAC and amp. $2,000 to way more than you need and while Focal makes great headphones there are much better options that will keep you under your budget for a complete setup.
I have Sennheiser HD6xx’s and a Topping DX3 Pro+, total cost under $500 including shipping and taxes. This combination is arguably as good as anything at any price point and they can produce all the bass you can handle up to hearing loss.
Don’t get lost in the weeds but I suggest you check out Audio Science Review on this topic. ASR has much more information and data on headphones, DAC’s and amps than this site although there are plenty of members here who can stear you in the right direction as well.
I absolutely DO NOT recommend buying a $2,000 pair of headphones a couple months into a hobby, as you gain experience and your personal taste matures you’ll discover what you like, starting off expensive can be a huge waste of money.