Background: Despite the rising interest of both academia and industry in microservice-based architectures and technical debt, the landscape remains uncharted when it comes to exploring the technical debt evolution in software systems built on this architecture. Aims: This study aims to unravel how technical debt evolves in software-intensive systems that utilize microservice architecture, focusing on (i) the patterns of its evolution, and (ii) the correlation between technical debt and the number of microservices. Method: We employ a mixed-method case study on an application with 13 microservices, 977 commits, and 38k lines of code. Our approach combines repository mining, automated code analysis, and manual inspection. The findings are discussed with the lead developer in a semi-structured interview, followed by a reflexive thematic analysis. Results: Despite periods of no TD growth, TD generally increases over time. TD variations can occur irrespective of microservice count or commit activity. TD and microservice numbers are often correlated. Adding or removing a microservice impacts TD similarly, regardless of existing microservice count. Conclusions: Developers must be cautious about the potential technical debt they might introduce, irrespective of the development activity conducted or the number of microservices involved. Maintaining steady technical debt during prolonged periods of time is possible, but growth, particularly during innovative phases, may be unavoidable. While monitoring technical debt is the key to start managing it, technical debt code analysis tools must be used wisely, as their output always necessitates also a qualitative system understanding to gain the complete picture.