This we can do in three steps:

Step 1 Get Account record data for that we need recordId which we have.

Step 2 Now get Segment_ID__c field value from account record.

Step 3 Finally get the loadPersonalizedOffers with the Segment_ID__c value.

Code will look something like this:

import { LightningElement, api, track, wire } from 'lwc';
import { getRecord } from 'lightning/uiRecordApi';

/* ... */

import loadPersonalizedOffers from "@salesforce/apex/PersonalizedOffersController.loadPersonalizedOffers";

FIELDS = ['Segment_ID__c'];

export default class Personalized_offers extends LightningElement {
    @api recordId;
    @track account;
    segmentId;
    
    /* ... */
    
    @wire(getRecord, { recordId: '$recordId', fields }) /* Step 1 */
    getAccount({error, data}){
        if (error) {            
            this.dispatchEvent(
                new ShowToastEvent({
                    title: 'Error loading account',
                    message: error.body.message,
                    variant: 'error',
                })
            );
        } else if (data) {
            this.account = data;
            this.segmentId = this.account.fields.Segment_ID__c.value; /* Step 2 */
            /* Now we can call the getPersonalizedOffers */
            loadPersonalizedOffers({Id: this.segmentId}).then((data)=> {
                if (data) {
                    console.log(JSON.stringify(data));
                }
            }).catch((error)=> {
               console.log(JSON.stringify(error));
            });
        }
    }

    /* ... */

}

This we can do in three steps:

Step 1 Get Account record data for that we need recordId which we have.

Step 2 Now get Segment_ID__c field value from account record.

Step 3 Finally get the loadPersonalizedOffers with the Segment_ID__c value.

Code will look something like this:

import { LightningElement, api, track, wire } from 'lwc';
import { getRecord } from 'lightning/uiRecordApi';

/* ... */

import loadPersonalizedOffers from "@salesforce/apex/PersonalizedOffersController.loadPersonalizedOffers";

FIELDS = ['Segment_ID__c'];

export default class Personalized_offers extends LightningElement {
    @api recordId;
    @track account;
    segmentId;
    
    /* ... */
    
    @wire(getRecord, { recordId: '$recordId', fields: FIELDS }) /* Step 1 */
    getAccount({error, data}){
        if (error) {            
            this.dispatchEvent(
                new ShowToastEvent({
                    title: 'Error loading account',
                    message: error.body.message,
                    variant: 'error',
                })
            );
        } else if (data) {
            this.account = data;
            this.segmentId = this.account.fields.Segment_ID__c.value; /* Step 2 */
            /* Now we can call the getPersonalizedOffers */
            loadPersonalizedOffers({Id: this.segmentId}).then((data)=> {
                if (data) {
                    console.log(JSON.stringify(data));
                }
            }).catch((error)=> {
               console.log(JSON.stringify(error));
            });
        }
    }

    /* ... */

}

This we can do in three steps:

Step 1 Get Account record data for that we need recordId which we have.

Step 2 Now get Segment_ID__c field value from account record.

Step 3 Finally get the loadPersonalizedOffers with the Segment_ID__c value.

Code will look something like this:

import { LightningElement, api, wire } from 'lwc';
import { getRecord } from 'lightning/uiRecordApi';

/* ... */

import loadPersonalizedOffers from "@salesforce/apex/PersonalizedOffersController.loadPersonalizedOffers";

FIELDS = ['Segment_ID__c'];

export default class Personalized_offers extends LightningElement {
    @api recordId;
    @track account;
    segmentId;
    
    /* ... */
    
    @wire(getRecord, { recordId: '$recordId', fields }) /* Step 1 */
    getAccount({error, data}){
        if (error) {            
            this.dispatchEvent(
                new ShowToastEvent({
                    title: 'Error loading account',
                    message: error.body.message,
                    variant: 'error',
                })
            );
        } else if (data) {
            this.account = data;
            this.segmentId = this.account.fields.Segment_ID__c.value; /* Step 2 */
            /* Now we can call the getPersonalizedOffers */
            @wire(loadPersonalizedOffers, {Id: this.segmentId}) personalizedOffers({error, data}) {
                if (data) {
                    console.log(JSON.stringify(data));
                }
            }
        }
    }

    /* ... */

}

This we can do in three steps:

Step 1 Get Account record data for that we need recordId which we have.

Step 2 Now get Segment_ID__c field value from account record.

Step 3 Finally get the loadPersonalizedOffers with the Segment_ID__c value.

Code will look something like this:

import { LightningElement, api, track, wire } from 'lwc';
import { getRecord } from 'lightning/uiRecordApi';

/* ... */

import loadPersonalizedOffers from "@salesforce/apex/PersonalizedOffersController.loadPersonalizedOffers";

FIELDS = ['Segment_ID__c'];

export default class Personalized_offers extends LightningElement {
    @api recordId;
    @track account;
    segmentId;
    
    /* ... */
    
    @wire(getRecord, { recordId: '$recordId', fields }) /* Step 1 */
    getAccount({error, data}){
        if (error) {            
            this.dispatchEvent(
                new ShowToastEvent({
                    title: 'Error loading account',
                    message: error.body.message,
                    variant: 'error',
                })
            );
        } else if (data) {
            this.account = data;
            this.segmentId = this.account.fields.Segment_ID__c.value; /* Step 2 */
            /* Now we can call the getPersonalizedOffers */
            loadPersonalizedOffers({Id: this.segmentId}).then((data)=> {
                if (data) {
                    console.log(JSON.stringify(data));
                }
            }).catch((error)=> {
               console.log(JSON.stringify(error));
            });
        }
    }

    /* ... */

}