Well, I tried those commands first having this modem in "disabled" state.
Then I enabled it using "mmcli -e -m 0" and drove those commands again and noticed differencies. It did not help. Putting those different settings to the same position as they are while modem is "registered" did not change anything.
Giving it AT+GCAP gives this list. I suppose it's a list of all commands this model supports:
+GCAP: AT,D,Q,V,A,H,Z,E,and_F,and_D,and_C,and_W,W,and_K,+CPAS,+CPIN,
+CBC,+CLIP,+CLIR,+CCFC,+CCWA,+CREG,+CRC,+VTS,+CHLD,+CLCC,+COPS,
+CSSN,+SIND,+SBCM,+CSQ,+CESQ,+CIMI,+CGMI,+CGMM,+CGSN,+CGMR,
+CMEE,+CSCS,+SMUX,+CPOF,S0,S2,S3,S4,S5,S6,S7,S8,S10,+CGDCONT,
+CGPCO,+CGQREQ,+CGQMIN,+CGATT,+CGACT,+CGPADDR,+CGCMOD,
+CGDATA,+CGAUTO,+CGANS,+CGCLASS,+CGEREP,+CGREG,+CGSMS,+SDATACONF,
+SDATASTART,+SDATASEND,+SSTRSEND,+SDATAREAD,+SDATARXMD,+CSMS,+CSDH,
+CRES,+CPMS,+CMGF,+CMGR,+CMGL,+CMGD,+CMGS,+CMSS,+CSMP,+CMGC,+CMGW,
+CSCA,+CSAS,+SMSC,+SUSS,+CSCB,+CNMI,+CPBR,+CPBF,+CPBW,+CPBP,+CPBN,
+CNUM,+SSMP,+CSVM,+CPBS,+COLP,+COLR,+CPUC,+CUSD,+CCUG,+CAOC,+CACM,
+STSF,+STIN,+STGR,+CAMM,+CCLK,+XX,+VTD,+CCID,+VGR,+CRSL,+CMUT,+VGT,
+SEQT,+SSEA,+SBAND,+SDTMF,+ECHO,+CLCK,+CPWD,+SSAM,+SSAP,+SADM,+CICB,
+CFUN,+IPR,+CIND,+CCED,+STONE,+CRMP,+SCDM,+SAC,+SSST,+SATT,+RFNVCHKS,
+S32K,+STMF,+CEER,+CR,+SAUTOATT,+SGPRSDATA,+SDCP,+SRWD,+SNVM,+SBOOT,
+SMGF,+SMGV,+SMGD,+SDMUT,+SLOG,+SUPS,+SSGF,+SSGS,+CPLS,+CPOL,xor_SYSINFO,
+CBST,+CMOD,DL,+CHUP,+CGDSCONT,+CGEQREQ,+CGEQMIN,
+CGTFT,+CMUX,xor_HVER,xor_SYSCONFIG,xor_SPN,+CSTA,xor_SCPBR,xor_SCPBW,
+ARMLOG,+SECMODE,+PSCUSTOMVER,xor_CARDMODE,+CRSM,+CNMA,+STED,
+CHUPVT,+TRACE,+OFF,+RESET,+CGEQNEG,+ECMMB,+ECMMBSTS,+ECMMBEER,
+EUICC,+ESQOPT,+CMMS,+ECPIN2,+ECIND,+EVTS,+CCWE,+BOOT,+CLVL,+CMER,
STAR_SPNTRG,+GMM,+FCLASS,+GCI,xor_DSCI,+PSRABR,+RRDMPARAM,
+TDMEASSWTH,+TRRPARAM,xor_SPEDGE,+L1PARAM,+ERGA,+ERTCA,+DMPARAMRESET,
+SMTIMER,+GRRTDNCELL,+GRRFDDNCELL,+NVOPERATE,
+SCPFRE,+PCCOTDCELL,STAR_SPPRAS,STAR_SPCSCN,STAR_SPENGI,STAR_SP3GPBR,
STAR_SPVTCS,+SIPCONFIG,xor_MBAU,xor_MBCELLID,+SFUN,+SADC,+CUFP,+CTZR,
+SMMSWAP,xor_FTDHO,xor_CURC,+WRRCPARAM,+SGMR,+TPCN,STAR_FDY,
+2GNCELL,+Q2GNCELL,+3GNCELL,+Q3GNCELL,+ALS,+SIPMODE,+NVSYNLINK,+SGFD,
+CSIM,+CCHC,+CCHO,+CGLA,+XMODEMACT,+CAGPS,+AGPSMR,+AGPSMER,
+SECUREBOOT,+SADMDSP,+SSYS,+SMS,+CPBCAPA,+TFSTAT,+XVOLLEV,+CVMOD,
+CUSATR,+CUSATW,+EMGONLYMODE,+GCAP,+GMI,+GSN,+BGLTEPLMN,+CEREG,
+CGCONTRDP,+CGSCONTRDP,+CGTFTRDP,+CGEQOS,+CGEQOSRDP,+ERSRP,
+CEMODE,+CSCON,+SCSFB,+CSSSFB,+AUTPWRON,+CPNER,+CSSAC,+RSIMRSP,
+VIRTUALSIMINIT,+COPSCSG,+LTESETRSRP,+LTEBGTIMER,+CEUS,+CGAUTH,
+CUSATT,+CUSATE,+CEVDP,+CAVIMS,+CMTLRA,+CGPIAF,+CASIMS,+CMMIVT,+CNAP,
+CPINR,+CPOS,+CTFR,+CPOSPARAM,+CMTLR,+CPOSR,xor_CMDVER,xor_RFSW,
+CNEM,+CEN,+ENGDISPLAY,+RRTMPARAM,+GRRLTEFREQ,+INSTANCEID,+IMEIURL,
+IMPU,+IMPI,+DOMAIN,+PCSCF,+IMSEN,+CIREG,+CLSSPDT,+CMCCS,+CLCCS,
+EMBMSIM,+CCMMD,+ISIM,+CMOLR,+MODECHAN,+FDDWRED,+PSISMSC,+CIREP,
+CISRVCC,+BSF,+XCAPRTURI,+CONFURI,+CCFCU,+APPSAUTHTYPE,+CGU,
+KEYSHORT,+FACTORST,+HEADINFO,+SYSSLEEP,+MAXPOWER,+FCBTTEST,
+FCMPTEST,+FCEPTEST,+TEMPTEST,+LOOPTEST,+SIMDETEC,+EMEMTEST,
+BATTTEST,+MSLSECUR,+IMEITEST,+AKSEEDNO,+CALIDATE,+LVOFLOCK,+DETALOCK,
+SERIALNO,+RSTVERIF,+LOCKREAD,+KSTRINGB,+SETTESTNV,+GETTESTNV,
+ARMLOGEVT,+LOGERASE,+SETFDATA,+GETFDATA,+GETFULLTESTNV,
+GETFULLHISTNV,+SETFULLFDATA,+GETFULLFDATA,+READRSSI,+BANSELCT,+SALRM,
+DTIME,+CDAT,+RTCCTEST,+VERSNAME,+CALLCONN,+DBGSCRN,+FACTOLOG,
+IMSITEST,+CDU,+XCAPIP,xor_SPDATAENCRYPT,xor_SPSIMLOCKDATAWRITE,
xor_SPSIMLOCKIMEI,
xor_SPHUK,xor_SPFACAUTHPUBKEY,xor_SPIDENTIFYSTART,xor_SPIDENTIFYEND,
+LTEPOWER,mod_MBMSCMD,mod_MBMSEV,+CEMBMSCNT,+CEMBMSCFG,+CDEFMP,
+VOWIFIEN,+IMSHO,+IMSHORST,+IMSHOWFINF,+IMSHOCALLEND,+VOWFREG,
+IMSWFATT,+IMSHODATAROUTER,+WIFIPARAM,+IMSCOUNTCFG,+CRLA,
+WRRDMPARAM,+VOWIFCALLINF,+COPN,+VOWIFIPCSCF,+MBMSEREG,+CSCM,
+IMSHONWINF,+PRENWINF,xor_LVDSDUMP,+ZCGMR,+ZRSSI,+ZPAS,+ZDON,
+ZCELLINFO,+HALOINFO,+GSMRXLEVELDBM,+WCDMARXLEVELDBM,
+LTERXLEVELDBM,+SMMFULL,+GTCGMR,+MHUP,+GTVTS,+GTCCINFO,+CMGLEX,
+NVRW,+COPNEX,+GTDTMF,+SMSREADY,+CALLBREAK,+GTSIMCNT,+CGCONTRDPEX,
+DUMPEN,+GTSDMUT,+GTRATPRIO,+GTBANDWIDTH,+PDPRETRY,+GTROAMST,
+GTCAINFO,+GTENMEASURE,+GTCELLLOCK,+GTPLMNLOCK,+GTMCSCQI,
+GTDATASTAT,+GTMTUEN,+GTANTINFO,+GTBWLIMIT,+ADVINFO,+GTDATATHROT
Any idea what to try next?
Or is there something else? Is it Luci that needs some kind of resetting/refreshing and not the modem?
What commands refresh Cellular Network WebUI?