Project-based learning improves student engagement and learning outcomes, yet allocating students to appropriately challenging projects while forming cognitively diverse teams remains difficult at scale. Traditional allocation methods (manual spreadsheets, preference surveys) can't construct the cognitively diverse teams that that collaborate cognitively. This mismatch perpetuates equity issues: high-performing students self-select visible projects while under-represented students face reduced access to opportunity. We propose TeamUp, a lightweight, embedding-based team-forming system designed to improve learning outcomes and equity in large-scale project-based courses. TeamUp uses semantic embeddings from pretrained language models to match students to projects aligned with their skill level. The system employs a hybrid ranking algorithm combining cosine similarity with pedagogical constraints (difficulty alignment, domain preferences, and demand balancing) to generate personalised and transparent recommendations. Beyond individual matching, TeamUp constructs cognitively diverse teams by modelling skill complementarity through embedding variance, ensuring teams possess well-distributed capabilities rather than homogeneous strengths. We evaluated TeamUp through a virtual experiment using 250 student profiles and 60 project descriptions. Results show: (1) substantially higher match quality (mean cosine similarity of 0.74 vs. 0.43); (2) better difficulty alignment (83% placed within one level vs. 34%); (3) more diverse teams (82% covering three or more technical areas vs. 41%); and (4) sub-second recommendation latency at operational costs under $0.10 per student.