Generally, you should start looking at the new Java API Client. Though it doesn't need to be immediately and you can also do a piece by piece migration if that makes it easier (see https://www.elastic.co/guide/en/elasticsearch/client/java-api-client/current/migrate-hlrc.html).
For your specific problem:
Since High-level Rest Client is now deprecated I am unable to resolve dependencies in order to use the HLRC existing code with Elasticsearch Version 8.x
What's the dependency you cannot resolve? Because the old HLRC should be able to work with 8.x — quote from the documentation link you've posted:
The High Level Client version 7.16 and higher can communicate with Elasticsearch version 8.x after enabling API compatibility mode. When this mode is enabled, the client will send HTTP headers that instruct Elasticsearch 8.x to honor 7.x request/responses.
And the new Java API Client also supports JDK 8 or newer, see https://www.elastic.co/guide/en/elasticsearch/client/java-api-client/current/installation.html.