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 1.3R_⊕and 3.0M_⊕. It is ideal for both transmission and emission spectroscopy and for testing interior models of telluric planets.Aims.To prepare for future studies, we aim to thoroughly characterise the planetary system with new accurate and precise data collected with state-of-the-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 telescope and CARMENES at the 3.5 m Calar Alto telescope, 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 atθ_LDD= 0.390 ± 0.018 mas. Together with a correctedGaiaEDR3 parallax, we obtain a stellar radiusR_*= 0.339 ± 0.015R_⊕. We also measure a stellar rotation period atP_rot= 49.9 ± 5.5 days, an upper limit to its XUV (5-920 A) flux informed by newHubble/STIS data, and, for the first time, a variety of element abundances (Fe, Mg, Si, V, Sr, Zr, Rb) and C/O ratio. Moreover, we imposed restrictive constraints on the presence of additional components, either stellar or sub-stellar, 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 atR_p= 1.343_−0.062^+0.063R_⊕andM_p= 3.00_−0.12^+0.13M_⊕, with relative uncertainties of the 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 forthcomingJames WebbSpace Telescope (Webb) observations.