Context. The Gl 486 system consists of a very nearby, relatively bright, weakly active M3.5 V star at just 8 pc with a warm transiting rocky planet of about 1.3 R ⊕ and 3.0 M ⊕ that is ideal for both transmission and emission spectroscopy and for testing interior models of telluric planets. Aims. To prepare for future studies, we thoroughly characterise the planetary system with new accurate and precise data collected with state-ofthe-art photometers from space and spectrometers and interferometers from the ground. Methods. We collected light curves of seven new transits observed with the CHEOPS space mission and new radial velocities obtained with MAROON-X at the 8.1 m Gemini North and CARMENES at the 3.5 m Calar Alto telescopes, together with previously published spectroscopic and photometric data from the two spectrographs and TESS. We also performed near-infrared interferometric observations with the CHARA Array and new photometric monitoring with a suite of smaller telescopes (AstroLAB, LCOGT, OSN, TJO). This extraordinary and rich data set was the input for our comprehensive analysis. Results. From interferometry, we measure a limb-darkened disc angular size of the star Gl 486 at θ LDD = 0.390 ± 0.018 mas. Together with a corrected Gaia EDR3 parallax, we obtain a stellar radius R = 0.339 ± 0.015 R . We also measure a stellar rotation period at P rot = 49.9 ± 5.5 d, an upper limit to its XUV (5-920 Å) flux with new Hubble/STIS data, and, for the first time, a variety of element abundances (Fe, Mg, Si, V, Sr, Zr, Rb) and C/O ratio. Besides, we impose restrictive constraints on the presence of additional components, either stellar or substellar, in the system. With the input stellar parameters and the radial-velocity and transit data, we determine the radius and mass of the planet Gl 486 b at R p = 1.343 +0.063 −0.062 R ⊕ and M p = 3.00 +0.13 −0.13 M ⊕ , with relative uncertainties in planet radius and mass of 4.7 % and 4.2 %, respectively. From the planet parameters and the stellar element abundances, we infer the most probable models of planet internal structure and composition, which are consistent with a relatively small metallic core with respect to the Earth, a deep silicate mantle, and a thin volatile upper layer. With all these ingredients, we outline prospects for Gl 486 b atmospheric studies, especially with forthcoming James Webb Space Telescope observations.