I am aware I can purchase the online Players handbook and in order to access to this background.

However, as I'm starting out I have currently bought the D&D Essentials Kit with the Dragon of Icespire Peak adventure. I have the physical copy and entered my code so I can access it online. So far I can access the suggested races, classes and backgrounds suggested in the physical book except for the Entertainer Background (page 25 in the book) .

I wondered if this was an accidental oversight as I thought I should be able to access everything in the book?

Thanks for any feedback.

The code for the essentials kit gives you access to the adventure here, not to the rules (including character options) in the kit, aside from those that are already free here. I think part of the idea here is the kit also includes a coupon for 50% off the PHB where the rest of this material can be found. To use the entertainer background, your choices are:

-homebrew it

-purchase just the background

-purchase the entire PHB (using the code from the kit for 50% off)

That makes sense I guess.

I just figured since the other backgrounds available in the book (there are only 5) are available in the website then this one would be too.

I can understand  why it seemed that way.  What is available for free here are those things that Wizards of the Coast makes available for free in pdfs, namely the Basic Rules, The System Reference Document (essentially an expanded version of the Basic Rules with licensing information for folks who want to use those elements in gaming aids they make), and the Elemental Evil Players Companion (an expansion/update that coincided with a specific adventure).  There are a few other things that are free, as well, but those three make the majority.  all the player options (like backgrounds, subclasses, spells, etc.) in the Basic Rules and SRD are also in the Players Handbook, but not everything in the Players' Handbook is in the free resources.  That can be confusing to new (and sometimes not so new) players.