Context. Transmission spectra of Neptune-sized exoplanets are frequently observed to be featureless at low-to-mid resolutions from space; whereas high-altitude clouds can mute spectral features, high atmospheric metallicities can also result in compressed envelopes, where low scale heights may also yield undetectable signatures. Aims. We aim to study the atmospheric properties of the warm Neptune GJ 436 b by combining a set of five transit events observed with the CARMENES spectrograph with one transit from CRIRES+ so as to provide the most constrained results possible at high resolution. Methods. We removed telluric and stellar signals from the data using SysRem and potential planetary signals were investigated using the cross-correlation technique. Following standard procedures for undetected species, we performed injection recovery tests and Bayesian retrievals to place constraints on the detectability of the main near-infrared absorbers. In addition, we simulated ELT/ANDES observations by computing end-to-end in silico datasets with EXoPLORE. Results. No molecular signals were detected in the atmosphere of GJ 436 b, which is consistent with previous studies. Combined CARMENES-CRIRES+ injection-recovery and Bayesian retrieval analyses show that the atmosphere is likely covered by high-altitude clouds (~1 mbar) at low and intermediate metallicities or, alternatively, is very metal-rich (≳ 900× solar), which would suppress spectral features without invoking clouds. Simulations of ELT/ANDES observations suggest a boost by nearly an order of magnitude to the upper limit in the photon-limited regime, reaching 0.1 mbar at 10-300× solar metallicities. Conclusions. The joint analysis of all useful transit observations from CARMENES and CRIRES+ provides the most stringent constraints to date on the atmospheric properties of GJ 436 b. Complementary CCF-based and retrieval approaches consistently indicate that the atmosphere is either cloudy or highly metal enriched. Any weak near-infrared absorption lines, if present, are likely to be below current detection limits. However, according to our simulations, these features may be revealed with ELT/ANDES even in single-transit observations.