This refers to the proficiency in academic language or language needed for…

Language proficiency researcher Jim Cummins divides a learner's language ability into two dimensions: Basic Interpersonal Communication Skills (BICS) — the conversational language used in everyday social interaction — and Cognitive Academic Language Proficiency (CALP) — the more abstract, decontextualised language required to learn and reason within academic content areas such as mathematics, science, and social studies.

The proficiency described in the question is defined purely in terms of academic language and the language demanded by different content areas, which is exactly how CALP is defined: it involves specialised, subject-specific vocabulary and complex sentence structures, and typically takes a learner about five to seven years to fully develop, compared to the one to two years usually needed for everyday conversational fluency.

• Inter-language proficiency describes the transitional grammar system a learner constructs while acquiring a second language, not a category of proficiency defined by academic-content demands.

• Basic Interpersonal Communication Skills (BICS) covers the conversational, context-embedded language of daily social exchange, which develops quickly and does not require content-area vocabulary.

• Communicative language proficiency is a general term for overall effectiveness in getting meaning across, without distinguishing between social and academic language demands.

So the term that matches the description is Cognitive Academic Language Proficiency (CALP).