OAuth 2.0 is both elegantly simple or extremely complex depending on your understanding of the technology and how to implement authorization.
I'm new to OAuth 2.0 and OpenIDConnect I want to ask if is it
necessary to implement OAuth 2.0 and OpenIDConnect for our login,
register flow of our own created client application (mobile apps and
server side app)?
No, it is not necessary to implement. There are many methods of authentication and authorization. OAuth is just one of the more popular methods.
A simpler and terrible method is to just implement username and passwords for your users. Simpler, in this case, is a relative term as now you need to worry about keeping usernames and passwords stored somewhere securely.
OAuth can be used to secure public access to your website, applications (REST endpoints), and more. OAuth can be used for server to server authorization. In the end, OAuth is just a method of creating a token that is presented to a service. The service verifies the access rights of that token and denies or proceeds with the request.
Authorization and Authentication are domains that require a lot of experience to implement correctly. There are many nuances to consider. That is why so many companies are breached, they do it wrong or implement weak methods. At one company I visited for an audit, I wrote down 10 usernames and passwords because everyone had yellow postit notes on their monitors. Even the best OAuth implementation will have problems with that level of security.