gives the series following

[Maybo]

Only Welcome To Wrexham has truly come close to replicating the cultural impact of Drive To Survive. The storytelling and access gives the series following the Ryan Reynolds and Rob McElhenney-owned Welsh club an authenticity that portrays the likes of Paul Mullin and Ollie Palmer as personalities, not just players. That it focused on the club’s impact on the city and its people was as big a draw as the behind-the-scene glimpses.

Source: MLS’s Netflix deal could be profound, if they’re willing to show the warts by Graham Ruthven, the Guardian

Have I understood the sentence correctly?

...gives the series following the series of the Ryan Reynolds..

 

[5jj]

No.

The storytelling and access gives the series following the Ryan Reynolds and Rob McElhenney-owned Welsh club an authenticity ...

The storytelling and access (subject) gives (verb) the series (direct object) which follows the Welsh club (which is owned by Ryan Reynolds and Rob McElhenney) an authenticity (direct object) ...

 

[jutfrank]

The storytelling and access (subject) gives (verb) the series which follows the Welsh club (which is owned by Ryan Reynolds and Rob McElhenney) (indirect object) an authenticity (direct object) ...

I think you slipped up there. The indirect object of gives is the series. It's the series that's has an authenticity, not the club.

The storytelling and access (subject) gives (verb) the series following the Ryan Reynolds and Rob McElhenney-owned Welsh club (indirect object) an authenticity ... (direct object)

@Maybo—The word following is like 'that follows'. The TV series follows the Welsh club.